SOLUTION: solve by elimination: 3x+5y=4 5x+2y=9

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Question 163048: solve by elimination:
3x+5y=4
5x+2y=9
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%283x%2B5y=4%2C5x%2B2y=9%29


5%283x%2B5y%29=5%284%29 Multiply the both sides of the first equation by 5.


15x%2B25y=20 Distribute and multiply.


-3%285x%2B2y%29=-3%289%29 Multiply the both sides of the second equation by -3.


-15x-6y=-27 Distribute and multiply.


So we have the new system of equations:
system%2815x%2B25y=20%2C-15x-6y=-27%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:


%2815x%2B25y%29%2B%28-15x-6y%29=%2820%29%2B%28-27%29


%2815x%2B-15x%29%2B%2825y%2B-6y%29=20%2B-27 Group like terms.


0x%2B19y=-7 Combine like terms. Notice how the x terms cancel out.


19y=-7 Simplify.


y=%28-7%29%2F%2819%29 Divide both sides by 19 to isolate y.


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15x%2B25y=20 Now go back to the first equation.


15x%2B25%28-7%2F19%29=20 Plug in y=-7%2F19.


15x-175%2F19=20 Multiply.


19%2815x-175%2Fcross%2819%29%29=19%2820%29 Multiply both sides by the LCD 19 to clear any fractions.


285x-175=380 Distribute and multiply.


285x=380%2B175 Add 175 to both sides.


285x=555 Combine like terms on the right side.


x=%28555%29%2F%28285%29 Divide both sides by 285 to isolate x.


x=37%2F19 Reduce.


So our answer is x=37%2F19 and y=-7%2F19.


Which form the ordered pair .


This means that the system is consistent and independent.