SOLUTION: solve for the value of X or Y algebraically. Show all your work. 2x+5y=12 3x+2y=7

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Question 281655: solve for the value of X or Y algebraically. Show all your work.
2x+5y=12
3x+2y=7
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%2B5y=12%2C3x%2B2y=7%29


3%282x%2B5y%29=3%2812%29 Multiply the both sides of the first equation by 3.


6x%2B15y=36 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%2B15y=36%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%2B15y%29%2B%28-6x-4y%29=%2836%29%2B%28-14%29


%286x%2B-6x%29%2B%2815y%2B-4y%29=36%2B-14 Group like terms.


0x%2B11y=22 Combine like terms.


11y=22 Simplify.


y=%2822%29%2F%2811%29 Divide both sides by 11 to isolate y.


y=2 Reduce.


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6x%2B15y=36 Now go back to the first equation.


6x%2B15%282%29=36 Plug in y=2.


6x%2B30=36 Multiply.


6x=36-30 Subtract 30 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%2B5y=12 (red) and 3x%2B2y=7 (green)