SOLUTION: solve by substitution method what is the solution of the system? 4x+3y=-11 and -8x+y=43

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Question 215115: solve by substitution method what is the solution of the system? 4x+3y=-11 and -8x+y=43
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%2B3y=-11%2C-8x%2By=43%29


-8x%2By=43 Start with the second equation.


y=43%2B8x Add 8x to both sides.


y=8x%2B43 Rearrange the terms and simplify.


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4x%2B3y=-11 Move back to the first equation.


4x%2B3%288x%2B43%29=-11 Plug in y=8x%2B43.


4x%2B24x%2B129=-11 Distribute.


28x%2B129=-11 Combine like terms on the left side.


28x=-11-129 Subtract 129 from both sides.


28x=-140 Combine like terms on the right side.


x=%28-140%29%2F%2828%29 Divide both sides by 28 to isolate x.


x=-5 Reduce.


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Since we know that x=-5, we can use this to find y.


-8x%2By=43 Move onto the second equation.


-8%28-5%29%2By=43 Plug in x=-5.


40%2By=43 Multiply.


y=43-40 Subtract 40 from both sides.


y=3 Combine like terms on the right side.


So the solutions are x=-5 and y=3.


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%2B3y=-11 (red) and -8x%2By=43 (green)