SOLUTION: Solve the given system by use of substitution: 3x+8y=66 -3x+y=15

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Question 202420: Solve the given system by use of substitution:

3x+8y=66
-3x+y=15
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system of equations:


system%283x%2B8y=66%2C-3x%2By=15%29


3x%2B8y=66 Start with the first equation.


8y=66-3x Subtract 3x from both sides.


y=%2866-3x%29%2F%288%29 Divide both sides by 8 to isolate y.


y=-%283%2F8%29x%2B33%2F4 Rearrange the terms and simplify.


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-3x%2By=15 Move onto the second equation.


-3x-%283%2F8%29x%2B33%2F4=15 Now plug in y=-%283%2F8%29x%2B33%2F4.


Multiply EVERY term by the LCD 8 to clear any fractions.


-24x-3x%2B66=120 Multiply and simplify.


-27x%2B66=120 Combine like terms on the left side.


-27x=120-66 Subtract 66 from both sides.


-27x=54 Combine like terms on the right side.


x=%2854%29%2F%28-27%29 Divide both sides by -27 to isolate x.


x=-2 Reduce.


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Since we know that x=-2, we can use this to find y.


3x%2B8y=66 Go back to the first equation.


3%28-2%29%2B8y=66 Plug in x=-2.


-6%2B8y=66 Multiply.


8y=66%2B6 Add 6 to both sides.


8y=72 Combine like terms on the right side.


y=%2872%29%2F%288%29 Divide both sides by 8 to isolate y.


y=9 Reduce.


So the solutions are x=-2 and y=9.


This means that the system is consistent and independent.


Notice when we graph the equations, we see that they intersect at . So this visually verifies our answer.


Graph of 3x%2B8y=66 (red) and -3x%2B1y=15 (green)