SOLUTION: Please help me understand how to solve these equations by the addition method. Many thanks. 2x = 2-y 3x + y = -1

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Question 335640: Please help me understand how to solve these equations by the addition method.
Many thanks.

2x = 2-y
3x + y = -1
Found 3 solutions by Fombitz, ankor@dixie-net.com, MarionR55:
Answer by Fombitz(32388)   (Show Source):
You can put this solution on YOUR website!

1.
2.
Add eq. 1 and eq. 2 to eliminate ,

Then use either equation to solve for .

Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website!
2x = 2 - y
3x + y = -1
:
We want both equation in the standard form (like the 2nd equation)
Put the 1st equation in the standard form
2x = 2 - y
add y to both sides and you have
2x + y = 2; the standard form
:
2x + y = 2
3x + y = -1
:
multiply the 1st equation by -1, then we can use the addition method
-2x - y = -2
+3x + y = -1
------------------addition eliminates y, find x
x = -3
:
Use the original 2nd equation to find y,
3x + y = -1
Replace x with - 3
3(-3) + y = -1
-9 + y = -1
add 9 to both sides
y = -1 + 9
y = 8
:
Check our solutions in the original 1st equation
2x = 2 - y
Replace x with -3 and y with 8
2(-3) = 2 - 8
-6 = -6, equality confirms our solution of x=-3, y=8
:
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Answer by MarionR55(1)   (Show Source):
You can put this solution on YOUR website!
2x = 2-y
3x + y = -1
move everything to the left hand side of the equation
2x + y - 2 = 0
3x + y + 1 = 0
now you want to add the lines together to get rid of the y yet they are bot positive so multiply by -1
-2x -y + 2 = 0
3x + y + 1 = 0 now add the lines together
______________
x + 3 = 0 solve for x
x= -3 now substitute -3 back in to the above equations and solve for y