SOLUTION: I need help using the echelon method to solve each of two equations in two unknowns. 2x + 7y = -8 -2x + 3y = -12

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Question 147639This question is from textbook
: I need help using the echelon method to solve each of two equations in two unknowns.
2x + 7y = -8
-2x + 3y = -12 This question is from textbook

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+%2B+7y+=+-8%2C-2x+%2B+3y+=+-12%29


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


%282x%2B7y%29%2B%28-2x%2B3y%29=%28-8%29%2B%28-12%29


%282x%2B-2x%29%2B%287y%2B3y%29=-8%2B-12 Group like terms.


0x%2B10y=-20 Combine like terms. Notice how the x terms cancel out.


10y=-20 Simplify.


y=%28-20%29%2F%2810%29 Divide both sides by 10 to isolate y.


y=-2 Reduce.


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2x%2B7y=-8 Now go back to the first equation.


2x%2B7%28-2%29=-8 Plug in y=-2.


2x-14=-8 Multiply.


2x=-8%2B14 Add 14 to both sides.


2x=6 Combine like terms on the right side.


x=%286%29%2F%282%29 Divide both sides by 2 to isolate x.


x=3 Reduce.


So our answer is x=3 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%2B7y=-8 (red) and -2x%2B3y=-12 (green)