SOLUTION: solve the systems of equations 5x+4y=6 -2x-3y=-1

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Question 210193: solve the systems of equations
5x+4y=6
-2x-3y=-1
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%2B4y=6%2C-2x-3y=-1%29


2%285x%2B4y%29=2%286%29 Multiply the both sides of the first equation by 2.


10x%2B8y=12 Distribute and multiply.


5%28-2x-3y%29=5%28-1%29 Multiply the both sides of the second equation by 5.


-10x-15y=-5 Distribute and multiply.


So we have the new system of equations:
system%2810x%2B8y=12%2C-10x-15y=-5%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:


%2810x%2B8y%29%2B%28-10x-15y%29=%2812%29%2B%28-5%29


%2810x%2B-10x%29%2B%288y%2B-15y%29=12%2B-5 Group like terms.


0x%2B-7y=7 Combine like terms.


-7y=7 Simplify.


y=%287%29%2F%28-7%29 Divide both sides by -7 to isolate y.


y=-1 Reduce.


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10x%2B8y=12 Now go back to the first equation.


10x%2B8%28-1%29=12 Plug in y=-1.


10x-8=12 Multiply.


10x=12%2B8 Add 8 to both sides.


10x=20 Combine like terms on the right side.


x=%2820%29%2F%2810%29 Divide both sides by 10 to isolate x.


x=2 Reduce.


So the solutions are x=2 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%2B4y=6 (red) and -2x-3y=-1 (green)