SOLUTION: Substitution method y=-3x+13 2x+9y=-8

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Question 218387: Substitution method
y=-3x+13
2x+9y=-8
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2x%2B9y=-8 Start with the second equation.


2x%2B9%28-3x%2B13%29=-8 Plug in y=-3x%2B13 into the second equation. In other words, replace each y with -3x%2B13. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.


2x%2B-27x%2B117=-8 Distribute


-25x%2B117=-8 Combine like terms on the left side


-25x=-8-117Subtract 117 from both sides


-25x=-125 Combine like terms on the right side


x=%28-125%29%2F%28-25%29 Divide both sides by -25 to isolate x


x=5 Divide


Now that we know that x=5, we can plug this into y=-3x%2B13 to find y


y=-3%285%29%2B13 Substitute 5 for each x


y=-2 Simplify


So our answer is x=5 and y=-2 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+-3x%2B13%2C+%28-8-2x%29%2F9%29+ Graph of and y=-3x%2B13 (red) and 2x%2B9y=-8 (green)