SOLUTION: Solve the system. 2x-3y=3 5x+2y=17

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Question 197571This question is from textbook Algebra and Trigonometry
: Solve the system.
2x-3y=3
5x+2y=17 This question is from textbook Algebra and Trigonometry

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%2C5x%2B2y=17%29


2%282x-3y%29=2%283%29 Multiply the both sides of the first equation by 2.


4x-6y=6 Distribute and multiply.


3%285x%2B2y%29=3%2817%29 Multiply the both sides of the second equation by 3.


15x%2B6y=51 Distribute and multiply.


So we have the new system of equations:
system%284x-6y=6%2C15x%2B6y=51%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%2815x%2B6y%29=%286%29%2B%2851%29


%284x%2B15x%29%2B%28-6y%2B6y%29=6%2B51 Group like terms.


19x%2B0y=57 Combine like terms.


19x=57 Simplify.


x=%2857%29%2F%2819%29 Divide both sides by 19 to isolate x.


x=3 Reduce.


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


4%283%29-6y=6 Plug in x=3.


12-6y=6 Multiply.


-6y=6-12 Subtract 12 from both sides.


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


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


y=1 Reduce.


So the solutions are x=3 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 2x-3y=3 (red) and 5x%2B2y=17 (green)