SOLUTION: y=x+3 8x-7y=12

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Question 144159: y=x+3
8x-7y=12
Found 3 solutions by jim_thompson5910, Alan3354, MathLover1:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given system
8x-7y=12
y=x%2B3



8x-7%28x%2B3%29=12 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.


8x-7x-21=12 Distribute


x-21=12 Combine like terms on the left side


x=12%2B21Add 21 to both sides


x=33 Combine like terms on the right side




Now that we know that x=33, we can plug this into y=x%2B3 to find y



y=%2833%29%2B3 Substitute 33 for each x


y=36 Simplify


So our answers are x=33 and y=36

Answer by Alan3354(69443) About Me  (Show Source):
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
y=x%2B3...write in standard form
8x-7y=12

+-x+%2B+y=3+...
8x-7y=12
Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


-x%2By=3

8x-7y=12





In order to graph these equations, we need to solve for y for each equation.




So let's solve for y on the first equation


-x%2By=3 Start with the given equation



1y=3%2Bx Add +x to both sides



1y=%2Bx%2B3 Rearrange the equation



y=%28%2Bx%2B3%29%2F%281%29 Divide both sides by 1



y=%28%2B1%2F1%29x%2B%283%29%2F%281%29 Break up the fraction



y=x%2B3 Reduce



Now lets graph y=x%2B3 (note: if you need help with graphing, check out this solver)



+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%2B3%29+ Graph of y=x%2B3




So let's solve for y on the second equation


8x-7y=12 Start with the given equation



-7y=12-8x Subtract 8+x from both sides



-7y=-8x%2B12 Rearrange the equation



y=%28-8x%2B12%29%2F%28-7%29 Divide both sides by -7



y=%28-8%2F-7%29x%2B%2812%29%2F%28-7%29 Break up the fraction



y=%288%2F7%29x-12%2F7 Reduce





Now lets add the graph of y=%288%2F7%29x-12%2F7 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%2B3%2C%288%2F7%29x-12%2F7%29+ Graph of y=x%2B3(red) and y=%288%2F7%29x-12%2F7(green)


From the graph, we can see that the two lines intersect at the point (33,36) (note: you might have to adjust the window to see the intersection)


graph%28600%2C600%2C+-15%2C50%2C-15%2C50%2Cx%2B3%2C%288%2F7%29x-12%2F7%29