SOLUTION: I actually attempted the examples in my book but still do not grasp the concept if I can actually get someone to get to break this down for me i might be able to do the rest on my
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Question 203481: I actually attempted the examples in my book but still do not grasp the concept if I can actually get someone to get to break this down for me i might be able to do the rest on my own:
y= -3x+19
y= 2x-1
and
x+3y=2
-x+y=1 thank you
Found 3 solutions by stanbon, ankor@dixie-net.com, jim_thompson5910:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
y= -3x+19
y= 2x-1
---
Substitute to get:
2x-1 = -3x+19
5x = 20
x = 4
===================================
and
x+3y=2
-x+y=1
---
Add the two equations to get:
4y = 3
y = 3/4
Substitute to solve for "x":
-x + (3/4) = 1
-x = 1/4
x = -1/4
-------------------------
Solution: (-1/4,3/4)
======================================
Cheers,
Stan H.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The first one lends itself to the substitution method
:
y= -3x+19
y= 2x - 1
Look at the 2nd equation, it should be apparent that we can
substitute (2x-1) for y in the 1st equation, then find x
2x - 1 = -3x + 19
2x + 3x = 19 + 1
5x = 20
x =
x = 4
Use the 2nd equation to find y. Substitute 4 for x
y = 2(4) - 1
y = 8 - 1
y = 7
Check your solutions by substitution in the 1st equation
y = - 3x + 19
7 = -3(4) + 19
7 = -12 + 19; confirms our solutions
:
:
The 2nd equation lends itself to the elimination method
x + 3y = 2
-x + y = 1
-------------adding these eliminates x, find y
0x + 4y = 3
y =
:
Find x using the 1st equation, substitute 3/4 of y
x + 3(3/4) = 2
x + 9/4 = 2
x = 2 - 9/4
x = -1/4
:
Check solution in the 2nd equation
-x + y = 1
-(-1/4) + (3/4) = 1
+1/4 + 3/4 = 1
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
# 1
Start with the first equation.
Plug in
Add to both sides.
Add to both sides.
Combine like terms on the left side.
Combine like terms on the right side.
Divide both sides by to isolate .
Reduce.
Now that we know the value of 'x', we can solve for 'y'
Go back to the first equation.
Plug in
Multiply
Combine like terms.
So the solutions are and .
Which form the ordered pair )
.
This means that the system is consistent and independent.
==================================================================
# 2
Start with the given system of equations:
Add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:
Group like terms.
Combine like terms. Notice how the x terms cancel out.
Simplify.
Divide both sides by to isolate .
------------------------------------------------------------------
Now go back to the first equation.
Plug in .
Multiply.
Multiply both sides by the LCD to clear any fractions.
Distribute and multiply.
Subtract 9 from both sides.
Combine like terms.
Divide both sides by to isolate .
So the solutions are and .
Which form the ordered pair )
.
This means that the system is consistent and independent.
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