# Questions on Algebra: Systems of Linear Equations answered by real tutors!

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 Linear Solvers Practice Answers archive Word Problems Lessons In depth

Question 751585: 2l+2w=228 L=w+42 How do you find the length(L) and width(w)?

Found 2 solutions by Cromlix, stanbon:
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2L + 2W = 228
L = W + 42
Substitute (w + 42) for L
2(W + 42) + 2W = 228
2W + 84 + 2W = 228
4W = 228 - 84
4W = 144
W = 36
Therefore Width = 36 and Length = (W + 42)
= 36 + 42 = 78
Hope this helps
:-)

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2l+2w=228 L=w+42 How do you find the length(L) and width(w)?
-----
Substitute for "L" and solve for "W":
2(W+42) + 2W = 228
W+42 + W = 114
2W = 72
Width = 36 units
----
Solve for "L"
L = W + 42
L = 78 units
==============
Cheers,
Stan H.
================

Question 750913: y=2x,y-2x=0

Found 2 solutions by jim_thompson5910, Alan3354:
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If you want to graph y=2x, then...

Looking at we can see that the equation is in slope-intercept form where the slope is and the y-intercept is note: really looks like

Since this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis

So we have one point

Now since the slope is comprised of the "rise" over the "run" this means

Also, because the slope is , this means:

which shows us that the rise is 2 and the run is 1. This means that to go from point to point, we can go up 2 and over 1

So starting at , go up 2 units

and to the right 1 unit to get to the next point

Now draw a line through these points to graph

So this is the graph of through the points and

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y=2x,y-2x=0
----------
Do you have a question?

Question 750822: Solve the system of equations. Enter your answer as an ordered pair.
5x - y = 27
5x + 4y = 42

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Solve the system of equations. Enter your answer as an ordered pair.
5x - y = 27
5x + 4y = 42
-----
Subtract to get:
5y = 15
y = 3
==========
Solve for "x":
5x - y = 27
5x -3 = 27
5x = 30
x = 6
============
Cheers,
Stan H.
============

Question 750732: how do I solve this equation?
-0.3(x-6)+ x = 0.5(3-x)

You can put this solution on YOUR website!
-0.3x+1.8+x=1.5-0.5x
-0.3x+0.5x+x=1.5-1.8
1.2x=-0.3
x=-0.3/1.2
x=-0.25

Question 750418: does 3x+7y=8 and 21y=-9x+24 have one solution, no solution or infinitly many solutions

Found 2 solutions by tommyt3rd, MathLover1:
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21y=-9x+24 can be rewritten as 9x+21y=24 and then 3x+7y=8. So it has the same graph (solution) as the first equation. So...many solutions

:)

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and

____________________solve the system

 Solved by pluggable solver: Solve the System of Equations by Graphing Start with the given system of equations: In order to graph these equations, we need to solve for y for each equation. So let's solve for y on the first equation Start with the given equation Subtract from both sides Rearrange the equation Divide both sides by Break up the fraction Reduce Now lets graph (note: if you need help with graphing, check out this solver) Graph of So let's solve for y on the second equation Start with the given equation Subtract from both sides Rearrange the equation Divide both sides by Break up the fraction Reduce Now lets add the graph of to our first plot to get: Graph of (red) and (green) From the graph, we can see that the two lines are identical (one lies perfectly on top of the other) and intersect at all points of both lines. So there are an infinite number of solutions and the system is dependent.

Question 750415: does 4x-3y=6 and 8x=6y+10 have one solution, no solution, or infinitley many solutions
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4x-3y=6
8x=6y+10 --> 4x-3y=5
-----------
Parallel lines, no intersection
--> no solution

Question 750317: 6X+8y=10
26x+48y=2
sir/mam, how to find the value of x and y....pls rply with full explaination..what isthe basic thing need to do for solving linear equation..pls rply.....am very poor in mathematics..

You can put this solution on YOUR website!
(1)6X+8y=10
(2)26x+48y=2
the basic thing to solve linear is making x variabel or y variabel gone.
In eq.1, you have 8y, and in eq.2 you have 48y. To solve it, multiply eq.1 with 6, so it will be 36x+48y=60. Look, y has the same variabel. All you have to do is subtracting it.
36x+48y=60
26x+48y=2
--------- -
10x=58
then, it's easy to find x
x=5,8
And yeah sorry for my english, i'm not a native English spearker :)
Cheers

Question 750119: Which of the coordinate pairs below is a solution to the following system of equations?
x2 + y2 = 18
5x + y = 17

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x2 + y2 = 18
5x + y = 17
--------------
No pairs are given.
---
Sub them into the linear eqn 1st.
If they fit, try the circle.
---
To solve it:
x2 + y2 = 18
5x + y = 17 -- y = 17 - 5x
----
sub for y in the circle

Solve for x, then for y.

Question 750104: The cost of 2 bagels and 2 cans of juice is $4.40. The cost of 3 bagels and 4 cans of juice is$7.80
a. write a system f equations to represent this situation.
b. Solve the system of equations by substitution. Explain what the solution means.

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2B+2J=440
3B+4J=780
Double both sides of first equation;
4B+4J=880
3B+4J=780 (and subtract the second equation from the first here)
B=100 A bagel is $1.00 2(100)+2J=440 200+2J=440 2J=240 J=120 Juice is$1.20

Question 750045: If you rent a car for 4 days, your bill will be $44. If you rent the same car for 10 days, your bill will be$100. Write an equation for the cost of the rental.
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using the first situation of (4,44)

:)

Question 749526: a rectangle has an area of 126 units ^2 and a perimeter of 46 units. Find the dimensions
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a rectangle has an area of 126 units ^2 and a perimeter of 46 units. Find the dimensions
-----------
9 by 14

Question 749517: How do you workout the problem x^2+9y^2=9
-2x+1y=-3 by elimination method

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x^2+9y^2=9
-2x+1y=-3 --> y = 2x-3
---------
Sub for y in the 1st eqn
x^2+9y^2=9

-------
 Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc) Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=1008 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 1.88850021260507, 1.03041870631385. Here's your graph:

=============
It might be called "elimination" since the y terms were eliminated by the substitution.

Question 749346: Solve 9x-3y=9, x+3y+11
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9x-3y=9,
x+3y=11

(9x-3y)+(x+3y)=9+11
9x +x = 20
10x=20
x=2

now using the 2nd equation

x+3y+11
2+3y=11
3y=9
y=3

solution: (2,3)

:)

Question 749059: if a+a+a=15 and is smiplified as 3a.what would h+h+h+h be?
You can put this solution on YOUR website!

if and is smiplified as
then =>
what would

Question 748673: What is the equation of the line that passes through (5, -2) and (-3, 4)?
You can put this solution on YOUR website!
 Solved by pluggable solver: Find the equation of line going through points hahaWe are trying to find equation of form y=ax+b, where a is slope, and b is intercept, which passes through points (x1, y1) = (5, -2) and (x2, y2) = (-3, 4). Slope a is . Intercept is found from equation , or . From that, intercept b is , or . y=(-0.75)x + (1.75) Your graph:

Question 748605: Solve the following system of equations.

5x - y = 7
2 + x = 7y

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5x - y = 7 ....1
x - 7y = -2 ....2
Multiply (2) by -5
5x - y = 7
-5x + 35y = 10
34y = 17
y = 17/34 or 1/2
Substitute y = 1/2 in (1)
5x - 1/2 = 7
5x = 7 + 1/2
5x = 15/2
x = 15/10 or 3/2
{3/2, 1/2}

Question 748492: two sums of y=x
y=-3x-8
I know on a linear graph they meet at co-ordinates (-2,-2)
ive been asked to solve the two above sums usng eliminaton and subsitution method for simultanious linear equations I have spent all day trying to work it out ad just cant grasp it could you help please

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y=x -------(A)
y=-3x-8 -------(B)
(A)-(B)
y-y = x-(-3x-8)
0 = x+3x+8
0 = 4x+8
dividing both side by 4
0 = x+2
so x = -2
substituting this into equation (A)
which is y=x
y=-2

Question 748164: is 9x+3y=12; 27x+9y=40 parallel, perpendicular, or neither?
Found 2 solutions by tommyt3rd, Cromlix:
You can put this solution on YOUR website!
We know that two lines are parallel if they have the same slope (and they are distinct). When the lines are in general form we'll use the formula m=-B/A to find their slopes with

first line: m=-3/9=-1/3
second line: m=-9/27=-1/3

these lines have the same slope and since we know that they are not the same line because

they must be parallel

:)

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9x + 3y = 12
3y = - 9x + 12
y = - 3x + 4 Gradient= -3
27x + 9y = 40
9y = - 27x + 40
y = - 3x + 40/9 Gradient = -3
Having the same gradients these lines are parallel

Question 747617:
the length of a rectangle is twice its width if the length decreases by 6cm and the width increases by 5 cm the rectangle becomes a square find the area of the rectangle

You can put this solution on YOUR website!
L=2W
(L-2)=(W+5)
(2W-2)=(W+5
2W-W=5+2
W=7 ANS.
L=2*7 ANS FOR THE RECTANGLE.
L=14 ANS. FOR THE RECTANGLE.
PROOF:
14-2=7+5
12=12 MAKES IT A SQUARE.
AREA=7*14=98 cm. IS THE AREA OF THE RECTANGLE.

A family refers to a group of two or more people related by birth, marriage, or adoption who reside together. In 2000, in Country A, the average family net worth was $240,000 and there were about 8.6 times 10^7 families. Calculate the total family net worth in Country A in 2000. Country A's total family net worth is __ dollars ( use scientific notation. Use the multiplication symbol in the math palette as needed, Round to the nearest tenth as needed. ) Answer by rothauserc(207) (Show Source): You can put this solution on YOUR website! We have 8.6 times 10^7 families and each family has a net worth of$240,000
so we have
(8.6*10^7)*(2.4*10^5)
add exponents with like base when multiplying
20.64*10^12

Question 747338: Solve by substitution.
X+3Y=15
2x-3y=3

Found 2 solutions by timvanswearingen, lynnlo:
You can put this solution on YOUR website!
To use substitution, you need to solve for one of the variables in terms of the other. I usually try to go for the easiest one, so I'm going to solve for x in the first equation.

Subtract 3y from both sides:

Now you have solved for x in terms of y.
Next, use the OTHER equation, not the one you used to solve for x.

Plug in 15-3y for x.

Distribute,

Combine like terms,

Subtract 30 from both sides,

Divide both sides by -9:

Now, plug in 3 for y into the equation where x is by itself.

Now you have x and y, so your answer is the ordered pair:

(6, 3)

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x=-12,,,,,,,,,,y=9

Question 747337: Solve by substitution.
3x-5y=4
y=4-2x

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3x-5y=4

3x-5(4-2x)=4 ... plug in y = 4 - 2x

3x-20+10x=4

13x-20=4

I'll let you finish. You need to solve for x. Once you find x, use it and plug it into y = 4 - 2x to find y.

Question 747335: What is the main disadvantage to graphing a system of equations?
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the solution is dependent upon precision and accuracy, so reliability is questionable

:)

simplify.
(8y)^-2= __ ( Use positive exponents only.)

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we take the reciprocal and we raise each factor of the base to the second power

Multiply and write the answer without exponents. ( the x's are actually standing for multiplication instead of a dot.)
(2 x 10^6) x(3 x 10^4)
=__

Found 2 solutions by tommyt3rd, josgarithmetic:
You can put this solution on YOUR website!
When the numbers are in scientific notation form we multiply the mantissas and add the exponents:
(2 x 10^6) x(3 x 10^4)=(2)(3)x 10^(6+4)=6 x 10^10

:)

You can put this solution on YOUR website!
Four factors, the associative and commutative properties and rule of exponents let us do this:

or as you are using,
6 x 10^10

Question 747258: Help me solve this equation please.
Simplify the expression

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8x^3(3x^2 + 5y)
= 24x^5 + 40x^3y
Simplified to:
4x^3(6x^2 + 10y)
Hope this helps

Question 747255: Help me solve this equation please.
Simplify the expression. Assume that all variables represent nonzero numbers.
6p^3 times 3p^5 = __

Question 746857: Find the solution to the system of equations given below by using linear combination:
8x + 4y = 48
4x – 2y = 40
A. (8, -4)
B.(11, 2)
C.(-8, 24)
D. (8, 4)

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8x + 4y = 48
4x – 2y = 40 MULTIPLY BY 2 & ADD
8X-4Y=80
8X+4Y=48
------------------
16X=128
X=128/16
X=8 ANS.
8*8+4Y=48
64+4Y=48
4Y=48-64
4Y=-16
Y=-4 ANS.
PROOF:
4*8-2*-4=40
32+8=40
40=40

Question 746901: how do you work it all out? how do you do the steps? how to solve it?
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how do you work it all out? how do you do the steps? how to solve it?
-----------
Work what out?

Question 745912: Sove graphicallt the system of Linear Equations: x+3y=11,3x+2y=12

You can put this solution on YOUR website!
Solve graphically the system of Linear Equations:
x+3y=11
3x+2y=12
------
Rearrange:
y = (-x+11)/3
y = (-3x +12)/2
------
Plot 2 points for each equation and draw a line thru them for each:
Points on 1st: (0, 3 1/3) ; (11,0)
Points on 2nd: (0,4) ; (4,0)
-----
Graph:

--------
Solution: (2,3)
--------
Cheers,
Stan H.

Question 745505: Please solve this system completely and show all work. Solve for x, y, and z.
x + 2y + z = 7
3x - y + z = -12
4x + 3y -2z = 9

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x + 2y + z = 7...............1
3x - y + z = -12..............2
4x + 3y -2z = 9...............3
eqn 2 X 2+eqn 1
x + 2y + z = 7...............1
6x - 2y + 2z = -24..............3
---------------------
7x +3z =-17.............5
eqn 2X 3 +eqn 3
9x -3y +3z = -36..............6
4x + 3y -2z = 9...............3
-----------------------
13x +z=-27..............7
eq5 - eqn 7 X 3
7x +3z =-17.............5
39x +3z=-81..............9
- - +
-----------
-32x=64
or x=-2
from eqn 5
7*(-2)+z=-17
or z=-17+14=-3
from eqn 1
-2 + 2y -3 = 7.
or 2y=7+5=12
or y=6

Question 745343: x= adult tickets y= children tickets
5x + 3y = 134
x + y = 32
a.) More adults attended the reunion than children
b.) six more children attended that adults
c.) nineteen children attended the reunion
d.) three more adults attended than children
i didnt know how i would solve this?

You can put this solution on YOUR website!
5x + 3y = 134
x + y = 32. multiply by -3
-3x-3y=-96
we get

2x=38
x=19
if x=17 plug x in x+y=32
y=13

children = 13
now you may find the correct statement

1/2x+3y=5/6
1/3x-5y=16/9

You can put this solution on YOUR website!
The problem states
1/2x+3y=5/6
1/3x-5y=16/9
we solve this using substitution since we have two equations and two unknowns
using equation one we multiply both sides of the = by 2 and we get
x+6y=5/3 and
x=5/3 - 6y
using the second equation we multiply both sides of the = by 3 and we get
x-15y=16/3
now substitute x with 5/3 - 6y and we get
5/3 - 6y - 15y = 16/3
-21y = 11/3
and y = (11/3) / -21 = -.17
and 1/2 * x + 3*-.17 = 5/6
multiply by 2 and we get
x + 6*-.17 = 5/3
x-1.02 = 1.67 and x = 2.69

Question 744909: Solve the following system of linear equations using either the substitution method or the addition method:
1. 2x+y=5
2. 4x+3y=14

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The problem states
Solve the following system of linear equations using either the substitution method or the addition method:
1. 2x+y=5
2. 4x+3y=14
using equation 1, we have y= 5-2x
substitute for y in equation 2 and we get
4x + 3*(5-2x) = 14
4x + 15-6x = 14
-2x = -1 then
x = 1/2 and 2*1/2 + y = 5 and y = 4

An investor invested a total of $1,800 in two mutual funds. One fund earned 9% profit while the other earned 3% profit. If the investor's total profit was$84, how much was invested in each mutual fund?

The amount invested in the mutual fund is earned 9% was $___ The amount invested in teh mutual fund that earned 3% was$___

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The problem states
An investor invested a total of $1,800 in two mutual funds. One fund earned 9% profit while the other earned 3% profit. If the investor's total profit was$84, how much was invested in each mutual fund?
let x = amount of money invested in 9% stock and
1800-x is amount of money invested in 3% stock
then we have
.09x + .03(1800 - x) = 84
.09x + 54 - .03x = 84
.06x = 30
x = 500
so $500 was invested at 9% and$1300 was invested at 3%

Use the elimination method to solve the system of equations
a+7b=7
a+2b=-3
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. There is one solution, it is __ ( simplify your answer. Type an ordered pair)
B. There are infinitely many solutions.
C. There is no solution.

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Use the elimination method to solve the system of equations
a+7b=7
a+2b=-3
----------- Subtract

Question 744363: I just need help doing system of equations... my teacher is telling me how but i just dont get how he gets all kinds of different #'s

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Use Google to see examples of systems of linear equations.
---
Or post a couple of your problems.
Cheers,
Stan H.
--------

Question 743980: 1. Which of the following is closest to one of the solutions of the equation x^2 + 6x - 11 = 0
a. –3
b. –1
c. 0
d. 2
2. How many real solutions does the equation x^2 + 4x - n^2 = 0 have?
a. none
b. one
c. two
d. cannot be determined
3. How many real solutions does the equation x^2 + bx + 4 = 0 have if b > 0?
a. none
b. one
c. two
d. cannot be determined

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I won't solve three problems in one post, so I'll just give you three hints. 1. Substitute each of the answer values given and do the arithmetic. The answer that gives the smallest absolute value result is the correct answer. 2. Whenever the and coefficients have opposite signs, two real and distinct roots are guaranteed. 3. In order to have any real roots where the and coefficients have the same sign, the value must be less than or equal to the value .

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it

Question 743176: 4(3t+1)=28