SOLUTION: Can you help me solve the system? x+2y=-12 y=20-2x

Question 227838: Can you help me solve the system?
x+2y=-12
y=20-2x
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
You can solve this by substitution or elimination.

I'll use elimination.

Your equations are:

x+2y = -12
y = 20-2x

Convert these equations into standard form.

x + 2y = -12 is already in standard form.

Take y = 20 - 2x

Add 2x to both sides to get:

2x + y = 20

Your two equations are now:

x + 2y = -12
2x + y = 20

Multiply both sides of the first equation by 2 to get:

2x + 4y = -24
2x + y = 20

subtract second equation from first to get:

3y = -44

divide both sides of equation by 3 to get:

y = -44/3

Replace y with -44/3 in first equation to get:

x+2y = -12 becomes:
x + 2*(-44/3) = -12
which becomes:
x - 88/3 = -12
multiply both sides of this equation by 3 to get:
3x - 88 = -36
add 88 to both sides of this equation to get:
3x = 88 - 36 = 52
divide both sides of this equation by 3 to get:
x = 52/3

you have:
y = -44/3
x = 52/3

Replace x and y in both original equations to confirm these answers are good.

x+2y = -12
y = 20-2x

become:

52/3 + 2*(-44/3) = -12

-44/3 = 20 - 2*(52/3)

first equation becomes 52/3 - 88/3 = - 12 which becomes -36/3 = -12 which becomes -12 = -12 which is true so the value for x and y are good.

second equation becomes -44/3 = 20 - 104/3 = 60/3 - 104/3 = -44/3 which is also true so the value for x and y are good in both equations.

your answers are:

y = -44/3

x = 52/3

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