SOLUTION: HOW WOULD I SOLVE THIS algebracially ? 3/4x-2/5y=2 1/2x-3/5y=-2

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Question 152235: HOW WOULD I SOLVE THIS algebracially ?

3/4x-2/5y=2
1/2x-3/5y=-2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%283%2F4%29x-%282%2F5%29y=2 Start with the first equation.


20%28%283%2Fcross%284%29%29x-%282%2Fcross%285%29%29y%29=20%282%29 Multiply both sides by the LCD 20 to clear any fractions.


15x-8y=40 Distribute and multiply.


%281%2F2%29x-%283%2F5%29y=-2 Move onto the second equation.


10%28%281%2Fcross%282%29%29x-%283%2Fcross%285%29%29y%29=10%28-2%29 Multiply both sides by the LCD 10 to clear any fractions.


5x-6y=-20 Distribute and multiply.


So we have the system of equations:


system%2815x-8y=40%2C5x-6y=-20%29



-3%285x-6y%29=-3%28-20%29 Multiply the both sides of the second equation by -3.


-15x%2B18y=60 Distribute and multiply.


So we have the new system of equations:
system%2815x-8y=40%2C-15x%2B18y=60%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-8y%29%2B%28-15x%2B18y%29=%2840%29%2B%2860%29


%2815x-15x%29%2B%28-8y%2B18y%29=40%2B60 Group like terms.


0x%2B10y=100 Combine like terms. Notice how the x terms cancel out.


10y=100 Simplify.


y=%28100%29%2F%2810%29 Divide both sides by 10 to isolate y.


y=10 Reduce.


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15x-8y=40 Now go back to the first equation.


15x-8%2810%29=40 Plug in y=10.


15x-80=40 Multiply.


15x=40%2B80 Add 80 to both sides.


15x=120 Combine like terms on the right side.


x=%28120%29%2F%2815%29 Divide both sides by 15 to isolate x.


x=8 Reduce.


So our answer is x=8 and y=10.


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 %283%2F4%29x-%282%2F5%29y=2 (red) and %281%2F2%29x-%283%2F5%29y=-2 (green)