SOLUTION: 2x + 3y = 8 and 3x + 2y = 7

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Question 197921This question is from textbook
: 2x + 3y = 8 and 3x + 2y = 7
This question is from textbook

Found 2 solutions by Ratman99, jim_thompson5910:
Answer by Ratman99(5) About Me  (Show Source):
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Ignore the other solution, I don't know what that is...




Start with the given system of equations:
system%282x%2B3y=8%2C3x%2B2y=7%29


3%282x%2B3y%29=3%288%29 Multiply the both sides of the first equation by 3.


6x%2B9y=24 Distribute and multiply.


-2%283x%2B2y%29=-2%287%29 Multiply the both sides of the second equation by -2.


-6x-4y=-14 Distribute and multiply.


So we have the new system of equations:
system%286x%2B9y=24%2C-6x-4y=-14%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%2B9y%29%2B%28-6x-4y%29=%2824%29%2B%28-14%29


%286x%2B-6x%29%2B%289y%2B-4y%29=24%2B-14 Group like terms.


0x%2B5y=10 Combine like terms.


5y=10 Simplify.


y=%2810%29%2F%285%29 Divide both sides by 5 to isolate y.


y=2 Reduce.


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6x%2B9y=24 Now go back to the first equation.


6x%2B9%282%29=24 Plug in y=2.


6x%2B18=24 Multiply.


6x=24-18 Subtract 18 from both sides.


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


x=%286%29%2F%286%29 Divide both sides by 6 to isolate x.


x=1 Reduce.


So the solutions are x=1 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%2B3y=8 (red) and 3x%2B2y=7 (green)