SOLUTION: Solve the following system of equations, and check: 2x+3y=-4 5x+2y=1

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Question 198423: Solve the following system of equations, and check:
2x+3y=-4
5x+2y=1

Found 2 solutions by jim_thompson5910, m.keenan:
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=-4%2C5x%2B2y=1%29


-2%282x%2B3y%29=-2%28-4%29 Multiply the both sides of the first equation by -2.


-4x-6y=8 Distribute and multiply.


3%285x%2B2y%29=3%281%29 Multiply the both sides of the second equation by 3.


15x%2B6y=3 Distribute and multiply.


So we have the new system of equations:
system%28-4x-6y=8%2C15x%2B6y=3%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:


%28-4x-6y%29%2B%2815x%2B6y%29=%288%29%2B%283%29


%28-4x%2B15x%29%2B%28-6y%2B6y%29=8%2B3 Group like terms.


11x%2B0y=11 Combine like terms.


11x=11 Simplify.


x=%2811%29%2F%2811%29 Divide both sides by 11 to isolate x.


x=1 Reduce.


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-4x-6y=8 Now go back to the first equation.


-4%281%29-6y=8 Plug in x=1.


-4-6y=8 Multiply.


-6y=8%2B4 Add 4 to both sides.


-6y=12 Combine like terms on the right side.


y=%2812%29%2F%28-6%29 Divide both sides by -6 to isolate y.


y=-2 Reduce.


So the solutions are x=1 and y=-2.


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=-4 (red) and 5x%2B2y=1 (green)

Answer by m.keenan(1) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the following system of equations, and check:
2x+3y=-4 (1)
5x+2y=1 (2) label equations
= 2x+3y=-4 (1) *2
5x+2y=1 (2) *3
=4x+6y=-8 (3)
15x+6y=3 (4) label new equations
Therefore: 4x+6y-(15x+6y)=-8-3
=4x+6y-15x-6y=-11
= -11x= =11
= x=1
Now we can sub x=1 back into any labelled equation.
2(1) +3y=-4
=3y=-6
y=-2