SOLUTION: 2x-3y=-3 x+6y=-9 What point makes both equations true?

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Question 177480This question is from textbook Algebra 1 concept and skills
: 2x-3y=-3
x+6y=-9
What point makes both equations true? This question is from textbook Algebra 1 concept and skills

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-3y=-3%2Cx%2B6y=-9%29


2%282x-3y%29=2%28-3%29 Multiply the both sides of the first equation by 2.


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


So we have the new system of equations:
system%284x-6y=-6%2Cx%2B6y=-9%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-6y%29%2B%28x%2B6y%29=%28-6%29%2B%28-9%29


%284x%2B1x%29%2B%28-6y%2B6y%29=-6%2B-9 Group like terms.


5x%2B0y=-15 Combine like terms.


5x=-15 Simplify.


x=%28-15%29%2F%285%29 Divide both sides by 5 to isolate x.


x=-3 Reduce.


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


4%28-3%29-6y=-6 Plug in x=-3.


-12-6y=-6 Multiply.


-6y=-6%2B12 Add 12 to both sides.


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


y=%286%29%2F%28-6%29 Divide both sides by -6 to isolate y.


y=-1 Reduce.


So our answer is x=-3 and y=-1.


Which form the ordered pair . This is the point that makes both equations true.


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-3y=-3 (red) and x%2B6y=-9 (green)