SOLUTION: Solve the following system of equations algebraically and check: 2x + 3y = 11 5x - 2y = -20

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Question 252501: Solve the following system of equations algebraically and check:
2x + 3y = 11
5x - 2y = -20
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%282x%2B3y=11%2C5x-2y=-20%29


2%282x%2B3y%29=2%2811%29 Multiply the both sides of the first equation by 2.


4x%2B6y=22 Distribute and multiply.


3%285x-2y%29=3%28-20%29 Multiply the both sides of the second equation by 3.


15x-6y=-60 Distribute and multiply.


So we have the new system of equations:
system%284x%2B6y=22%2C15x-6y=-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:


%284x%2B6y%29%2B%2815x-6y%29=%2822%29%2B%28-60%29


%284x%2B15x%29%2B%286y%2B-6y%29=22%2B-60 Group like terms.


19x%2B0y=-38 Combine like terms.


19x=-38 Simplify.


x=%28-38%29%2F%2819%29 Divide both sides by 19 to isolate x.


x=-2 Reduce.


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4x%2B6y=22 Now go back to the first equation.


4%28-2%29%2B6y=22 Plug in x=-2.


-8%2B6y=22 Multiply.


6y=22%2B8 Add 8 to both sides.


6y=30 Combine like terms on the right side.


y=%2830%29%2F%286%29 Divide both sides by 6 to isolate y.


y=5 Reduce.


So the solutions are x=-2 and y=5.


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 2x%2B3y=11 (red) and 5x-2y=-20 (green)