SOLUTION: how do you solve ...y=x+1 2x+y=7

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: how do you solve ...y=x+1 2x+y=7      Log On


   

Question 124846: how do you solve ...y=x+1
2x+y=7
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given system
2x%2B1y=7
y=x%2B1



2x%2B1%28x%2B1%29=7 Plug in y=x%2B1 into the first equation. In other words, replace each y with x%2B1. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.


2x%2B1x%2B1=7 Distribute


3x%2B1=7 Combine like terms on the left side


3x=7-1Subtract 1 from both sides


3x=6 Combine like terms on the right side


x=%286%29%2F%283%29 Divide both sides by 3 to isolate x



x=2 Divide




Now that we know that x=2, we can plug this into y=x%2B1 to find y



y=%282%29%2B1 Substitute 2 for each x


y=3 Simplify


So our answer is x=2 and y=3 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+-5%2C+5%2C+-5%2C+5%2C+7-2x%2C+x%2B1%29+ Graph of 2x%2B1y=7 (red) and y=x%2B1 (green)