# 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)

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**

**2x - 3y = 5 ---------------(i)**

**3x - (2y-3)/5 = 4 -------(ii)**

From eqn ---( i )

3y = 2x-5

## => y =(2x-5)/3 ---- (iii)

=>2y = (4x-10)/3

=>2y - 3 = (4x - 10)/3 - 3

= (4x -10- 9)/3

= ( 4x -19 )/3

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

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

**Now, 3x - (4x - 19 )/15 = 4**

** => 45x - 4x +19 = 60**

** => 41x= 41**

** => x= 1**

**From eqn ---(iii)**

** y= (2*1 - 5 )/3**

** = -3/3 = - 1**

**(x,y) = (1, -1) -------- solutiom.**