SOLUTION: X=2y-7 3X +2y=-5 use addition method

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Question 146700: X=2y-7
3X +2y=-5
use addition method
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%28x=2y-7%2C3x%2B2y=-5%29


x=2y-7 Start with the first equation.


x-2y=-7 Subtract 2y from both sides.


So we have the new system of equations:

system%28x-2y=-7%2C3x%2B2y=-5%29


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


%28x-2y%29%2B%283x%2B2y%29=%28-7%29%2B%28-5%29


%281x%2B3x%29%2B%28-2y%2B2y%29=-7%2B-5 Group like terms.


4x%2B0y=-12 Combine like terms. Notice how the y terms cancel out.


4x=-12 Simplify.


x=%28-12%29%2F%284%29 Divide both sides by 4 to isolate x.


x=-3 Reduce.


------------------------------------------------------------------


x-2y=-7 Now go back to the first equation.


-3-2y=-7 Plug in x=-3.


-3-2y=-7 Multiply.


-2y=-7%2B3 Add 3 to both sides.


-2y=-4 Combine like terms on the right side.


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


y=2 Reduce.


So our answer is x=-3 and y=2.


Which form the ordered pair .


This means that the two equations are consistent and independent.


Notice when we graph the equations, we see that they intersect at . So this visually verifies our answer.


Graph of x-2y=-7 (red) and 3x%2B2y=-5 (green)