Solve the following by elimination method: 2x - 3y = 5 3x - (2y-3)/5 = 4  

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(1) 2x-3y=5
(2) 3x-(2y-3)/5=4

Simplify (2)
(5)3x - (5)(2y-3)/5 = 4(5)
15x - 2y + 3 = 20
(3) 15x - 2y = 17

2x - 3y = 5 multiply by -2 to get -4x + 6y = -10   (4)
15x - 2y = 23 multiply by 3 to get 45x - 6y = 51   (5)

Now add (4) and (5) to get

41x = 41  and solving for x we get

x = 1

To find y we substitute x = 1 into (1) and solve for y
2(1)-3y=5

3y = 2 - 5
3y = -3
y = -1

Check the answers in the 2nd equation
3x-(2y-3)/5=4
3(1) - (2(-1)-3)/5 = 4
3 - (-5)/5 = 4
3 - (-1) = 4
4 = 4  Checks...

So our answer is (1, -1)

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We have to solve by elimination the set of equations:

2x - 3y = 5 ...(1)

3x - (2y-3)/5 = 4 ...(2)

3*(1) - 2*(2)

=> 6x - 9y - 6x + 2*(2y-3)/5 = 15 - 8

=> -9y + (2/5)(2y - 3) = 7

=> -45y + 4y - 6 = 35

=> -41y = 41

=> y = -1

(2)

=> 15x - 2y + 3 = 20

=> 15x - 2y = 17 ...(3)

2*(1) - 3*(3)

=> 4x - 6y - 45x + 6y = 10 - 51

=> -41x = -41

=> x = 1

The solution is x = 1 and y = -1

Approved by eNotes Editorial Team
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