SOLUTION: 4x+3y=-8 -8x+y=-12

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Question 1113495: 4x+3y=-8
-8x+y=-12
Found 3 solutions by Alan3354, MathLover1, MathTherapy:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Multiply the 1st eqn by 2, then add them.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

4x%2B3y=-8+
-8x%2By=-12
-----------------------------
Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


4x%2B3y=-8

-8x%2By=-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


4x%2B3y=-8 Start with the given equation



3y=-8-4x Subtract 4+x from both sides



3y=-4x-8 Rearrange the equation



y=%28-4x-8%29%2F%283%29 Divide both sides by 3



y=%28-4%2F3%29x%2B%28-8%29%2F%283%29 Break up the fraction



y=%28-4%2F3%29x-8%2F3 Reduce



Now lets graph y=%28-4%2F3%29x-8%2F3 (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+%28-4%2F3%29x-8%2F3%29+ Graph of y=%28-4%2F3%29x-8%2F3




So let's solve for y on the second equation


-8x%2By=-12 Start with the given equation



1y=-12%2B8x Add 8+x to both sides



1y=%2B8x-12 Rearrange the equation



y=%28%2B8x-12%29%2F%281%29 Divide both sides by 1



y=%28%2B8%2F1%29x%2B%28-12%29%2F%281%29 Break up the fraction



y=8x-12 Reduce





Now lets add the graph of y=8x-12 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%28-4%2F3%29x-8%2F3%2C8x-12%29+ Graph of y=%28-4%2F3%29x-8%2F3(red) and y=8x-12(green)


From the graph, we can see that the two lines intersect at the point (1,-4) (note: you might have to adjust the window to see the intersection)

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

4x+3y=-8
-8x+y=-12
Multiply eq (i) by 2 to get eq (iii)

Add eqs (ii) & (iii) to ELIMINATE x and get the value of y

Substitute value of y into any of the 2 ORIGINAL equations [eq (i) or (ii)] to get the value of x.

That's it! Nothing COMPLEX nor LENGTHY!