SOLUTION: solve each system of linear equations by addition or elimination 2) 2x + y = 5 3x - 3y = 3

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Question 241745: solve each system of linear equations by addition or elimination

2) 2x + y = 5
3x - 3y = 3
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%2By=5%2C3x-3y=3%29


3%282x%2By%29=3%285%29 Multiply the both sides of the first equation by 3.


6x%2B3y=15 Distribute and multiply.


So we have the new system of equations:
system%286x%2B3y=15%2C3x-3y=3%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:


%286x%2B3y%29%2B%283x-3y%29=%2815%29%2B%283%29


%286x%2B3x%29%2B%283y-3y%29=15%2B3 Group like terms.


9x%2B0y=18 Combine like terms.


9x=18 Simplify.


x=%2818%29%2F%289%29 Divide both sides by 9 to isolate x.


x=2 Reduce.


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6x%2B3y=15 Now go back to the first equation.


6%282%29%2B3y=15 Plug in x=2.


12%2B3y=15 Multiply.


3y=15-12 Subtract 12 from both sides.


3y=3 Combine like terms on the right side.


y=%283%29%2F%283%29 Divide both sides by 3 to isolate y.


y=1 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 2x%2By=5 (red) and 3x-3y=3 (green)