SOLUTION: i need to solve this question algebracially 3/4x-2/5y=2 1/2x-3/5y=-2

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Question 152103: i need to solve this question algebracially
3/4x-2/5y=2
1/2x-3/5y=-2
Answer by Fombitz(13823) About Me  (Show Source):
You can put this solution on YOUR website!
1.%283%2F4%29x-%282%2F5%29y=2
2.%281%2F2%29x-%283%2F5%29y=-2
I'm not a big fan of fractions so I usually multiply both equations to get rid of denominators.
Multiply eq. 1 by 20 and eq. 2 by 10.
1.20%283%2F4%29x-20%282%2F5%29y=20%282%29
1.15x-8y=40
.
.
.
2.10%281%2F2%29x-10%283%2F5%29y=10%28-2%29
2.5x-6y=-20
Now use the elimination method to solve.
If I multiply eq. 2 by (-3) and add to eq. 1, I can get rid of x,
%2815x-8y%29%2B%28-3%29%285x-6y%29=40%2B%28-3%29%28-20%29
%2815x-8y%29%2B%28-15x%2B18y%29=40%2B60
10y=100
highlight%28y=10%29
Using eq. 1,
1.15x-8y=40
15x-8%2810%29=40
15x-80=40
15x=120
highlight%28x=8%29
.
.
.
Check the answer with the original equations.
1.%283%2F4%29x-%282%2F5%29y=2
%283%2F4%29%288%29-%282%2F5%29%2810%29=2
6-4=2
2=2
True.
I'll leave it to you to verify that eq. 2 works also.