SOLUTION: 5x+3y=7 x-6y=8

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Question 201106: 5x+3y=7
x-6y=8
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%285x%2B3y=7%2Cx-6y=8%29


2%285x%2B3y%29=2%287%29 Multiply the both sides of the first equation by 2.


10x%2B6y=14 Distribute and multiply.


So we have the new system of equations:
system%2810x%2B6y=14%2Cx-6y=8%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%2B6y%29%2B%28x-6y%29=%2814%29%2B%288%29


%2810x%2Bx%29%2B%286y-6y%29=14%2B8 Group like terms.


11x%2B0y=22 Combine like terms.


11x=22 Simplify.


x=%2822%29%2F%2811%29 Divide both sides by 11 to isolate x.


x=2 Reduce.


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10x%2B6y=14 Now go back to the first equation.


10%282%29%2B6y=14 Plug in x=2.


20%2B6y=14 Multiply.


6y=14-20 Subtract 20 from both sides.


6y=-6 Combine like terms on the right side.


y=%28-6%29%2F%286%29 Divide both sides by 6 to isolate y.


y=-1 Reduce.


So the solutions are x=2 and y=-1.


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 5x%2B3y=7 (red) and x-6y=8 (green)