SOLUTION: y=x+3 -7x-y=1

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Question 120449: y=x+3
-7x-y=1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given system
-7x-y=1
y=x%2B3



-7x-%28x%2B3%29=1 Plug in y=x%2B3 into the first equation. In other words, replace each y with x%2B3. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.


-7x-x-3=1 Distribute the negative


-8x-3=1 Combine like terms on the left side


-8x=1%2B3Add 3 to both sides


-8x=4 Combine like terms on the right side


x=%284%29%2F%28-8%29 Divide both sides by -8 to isolate x



x=-1%2F2 Reduce




Now that we know that x=-1%2F2, we can plug this into y=x%2B3 to find y



y=%28-1%2F2%29%2B3 Substitute -1%2F2 for each x


y=5%2F2 Combine like terms


So our answer is x=-1%2F2 and y=5%2F2 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+%281%2B7x%29%2F-1%2C+x%2B3%29+ Graph of -7x-y=1 (red) and y=x%2B3 (green)