SOLUTION: Solve the given system by use of substitution: 4x+5y=8 -6x+y=56

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Question 202419: Solve the given system by use of substitution:

4x+5y=8
-6x+y=56
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%284x%2B5y=8%2C-6x%2By=56%29


4x%2B5y=8 Start with the first equation.


5y=8-4x Subtract 4x from both sides.


y=%288-4x%29%2F%285%29 Divide both sides by 5 to isolate y.


y=-%284%2F5%29x%2B8%2F5 Rearrange the terms and simplify.


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-6x%2By=56 Move onto the second equation.


-6x-%284%2F5%29x%2B8%2F5=56 Now plug in y=-%284%2F5%29x%2B8%2F5.


Multiply EVERY term by the LCD 5 to clear any fractions.


-30x-4x%2B8=280 Multiply and simplify.


-34x%2B8=280 Combine like terms on the left side.


-34x=280-8 Subtract 8 from both sides.


-34x=272 Combine like terms on the right side.


x=%28272%29%2F%28-34%29 Divide both sides by -34 to isolate x.


x=-8 Reduce.


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Since we know that x=-8, we can use this to find y.


4x%2B5y=8 Go back to the first equation.


4%28-8%29%2B5y=8 Plug in x=-8.


-32%2B5y=8 Multiply.


5y=8%2B32 Add 32 to both sides.


5y=40 Combine like terms on the right side.


y=%2840%29%2F%285%29 Divide both sides by 5 to isolate y.


y=8 Reduce.


So the solutions are x=-8 and y=8.


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 4x%2B5y=8 (red) and -6x%2By=56 (green)