SOLUTION: 10x-8y=negative46 x+2y=1

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Question 177388: 10x-8y=negative46
x+2y=1
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%2810x-8y=-46%2Cx%2B2y=1%29


4%28x%2B2y%29=4%281%29 Multiply the both sides of the second equation by 4.


4x%2B8y=4 Distribute and multiply.


So we have the new system of equations:
system%2810x-8y=-46%2C4x%2B8y=4%29


Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


%2810x-8y%29%2B%284x%2B8y%29=%28-46%29%2B%284%29


%2810x%2B4x%29%2B%28-8y%2B8y%29=-46%2B4 Group like terms.


14x%2B0y=-42 Combine like terms.


14x=-42 Simplify.


x=%28-42%29%2F%2814%29 Divide both sides by 14 to isolate x.


x=-3 Reduce.


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10x-8y=-46 Now go back to the first equation.


10%28-3%29-8y=-46 Plug in x=-3.


-30-8y=-46 Multiply.


-8y=-46%2B30 Add 30 to both sides.


-8y=-16 Combine like terms on the right side.


y=%28-16%29%2F%28-8%29 Divide both sides by -8 to isolate y.


y=2 Reduce.


So our answer is x=-3 and y=2.


Which form the ordered pair .


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 10x-8y=-46 (red) and x%2B2y=1 (green)