SOLUTION: Solve the system by substitution. 2x – 4y = 18 y = –x – 12

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Question 124717: Solve the system by substitution.
2x – 4y = 18
y = –x – 12
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given system
2x-4y=18
y=-x-12



2x-4%28-x-12%29=18 Plug in y=-x-12 into the first equation. In other words, replace each y with -x-12. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.


2x%2B4x%2B48=18 Distribute


6x%2B48=18 Combine like terms on the left side


6x=18-48Subtract 48 from both sides


6x=-30 Combine like terms on the right side


x=%28-30%29%2F%286%29 Divide both sides by 6 to isolate x



x=-5 Divide




Now that we know that x=-5, we can plug this into y=-1x-12 to find y



y=-%28-5%29-12 Substitute -5 for each x


y=-7 Simplify


So our answer is x=-5 and y=-7 which also looks like



Notice if we graph the two equations, we can see that their intersection is at . So this verifies our answer.


+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+%2818-2x%29%2F%28-4%29%2C+-x-12%29+ Graph of 2x-4y=18 (red) and y=-x-12 (green)