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)   (Show Source): You can put this solution on YOUR website!

Start with the given system of equations:



Multiply the both sides of the second equation by -5.


Distribute and multiply.


So we have the new system of equations:



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





Group like terms.


Combine like terms. Notice how the x terms cancel out.


Simplify.


Divide both sides by to isolate .


Reduce.


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Now go back to the first equation.


Plug in .


Multiply.


Subtract from both sides.


Combine like terms on the right side.


Divide both sides by to isolate .


Reduce.


So our answer is and .


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 (red) and (green)

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