SOLUTION: 5x+2y=8 2x-3y=7

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Question 184023: 5x+2y=8
2x-3y=7
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%2B2y=8%2C2x-3y=7%29


3%285x%2B2y%29=3%288%29 Multiply the both sides of the first equation by 3.


15x%2B6y=24 Distribute and multiply.


2%282x-3y%29=2%287%29 Multiply the both sides of the second equation by 2.


4x-6y=14 Distribute and multiply.


So we have the new system of equations:
system%2815x%2B6y=24%2C4x-6y=14%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:


%2815x%2B6y%29%2B%284x-6y%29=%2824%29%2B%2814%29


%2815x%2B4x%29%2B%286y%2B-6y%29=24%2B14 Group like terms.


19x%2B0y=38 Combine like terms.


19x=38 Simplify.


x=%2838%29%2F%2819%29 Divide both sides by 19 to isolate x.


x=2 Reduce.


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15x%2B6y=24 Now go back to the first equation.


15%282%29%2B6y=24 Plug in x=2.


30%2B6y=24 Multiply.


6y=24-30 Subtract 30 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%2B2y=8 (red) and 2x-3y=7 (green)