SOLUTION: Solve each of the following systems by substitution: 5x - 6y = 21 x - 2y = 5

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Question 164090: Solve each of the following systems by substitution:
5x - 6y = 21
x - 2y = 5
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-6y=21%2Cx-2y=5%29


-5%28x-2y%29=-5%285%29 Multiply the both sides of the second equation by -5.


-5x%2B10y=-25 Distribute and multiply.


So we have the new system of equations:
system%285x-6y=21%2C-5x%2B10y=-25%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:


%285x-6y%29%2B%28-5x%2B10y%29=%2821%29%2B%28-25%29


%285x%2B-5x%29%2B%28-6y%2B10y%29=21%2B-25 Group like terms.


0x%2B4y=-4 Combine like terms. Notice how the x terms cancel out.


4y=-4 Simplify.


y=%28-4%29%2F%284%29 Divide both sides by 4 to isolate y.


y=-1 Reduce.


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5x-6y=21 Now go back to the first equation.


5x-6%28-1%29=21 Plug in y=-1.


5x%2B6=21 Multiply.


5x=21-6 Subtract 6 from both sides.


5x=15 Combine like terms on the right side.


x=%2815%29%2F%285%29 Divide both sides by 5 to isolate x.


x=3 Reduce.


So our answer is x=3 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-6y=21 (red) and x-2y=5 (green)