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) About Me  (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) About Me  (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 = 20%2F5
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 = 3%2F4
:
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) About Me  (Show Source):
You can put this solution on YOUR website!
# 1

y=-3x%2B19 Start with the first equation.


2x-1=-3x%2B19 Plug in y=2x-1


2x=-3x%2B19%2B1 Add 1 to both sides.


2x%2B3x=19%2B1 Add 3x to both sides.


5x=19%2B1 Combine like terms on the left side.


5x=20 Combine like terms on the right side.


x=%2820%29%2F%285%29 Divide both sides by 5 to isolate x.


x=4 Reduce.


Now that we know the value of 'x', we can solve for 'y'


y=-3x%2B19 Go back to the first equation.


y=-3%284%29%2B19 Plug in x=4


y=-12%2B19 Multiply


y=7 Combine like terms.


So the solutions are x=4 and y=7.


Which form the ordered pair .


This means that the system is consistent and independent.



==================================================================

# 2

Start with the given system of equations:
system%28x%2B3y=2%2C-x%2By=1%29


Add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


%28x%2B3y%29%2B%28-x%2By%29=%282%29%2B%281%29


%28x-x%29%2B%283y%2By%29=2%2B1 Group like terms.


0x%2B4y=3 Combine like terms. Notice how the x terms cancel out.


4y=3 Simplify.


y=3%2F4 Divide both sides by 4 to isolate y.


------------------------------------------------------------------


x%2B3y=2 Now go back to the first equation.


x%2B3%283%2F4%29=2 Plug in y=3%2F4.


x%2B9%2F4=2 Multiply.


4%28x%2B9%2Fcross%284%29%29=4%282%29 Multiply both sides by the LCD 4 to clear any fractions.


4x%2B9=8 Distribute and multiply.


4x=8-9 Subtract 9 from both sides.


4x=-1 Combine like terms.


x=-1%2F4 Divide both sides by 3 to isolate x.


So the solutions are x=-1%2F4 and y=3%2F4.


Which form the ordered pair .


This means that the system is consistent and independent.