# 2x - 3y = 12 and 3x + 4y = 15 using substitution and elimination

Substitution method :

Given  equations are

2x - 3y  = 12  ---> (1)

3x + 4y = 15  ---> (2)

Solve for y from (2).

4y = 15 - 3x

y = (15 - 3x)/4.  ---> (3)

From (3) substitute the y value in equation (1).

2x - 3(15 - 3x)/4  = 12

Combine like terms uisng distributive property.

8x - 45 + 9x = 48

Sepereate variables and constants.

17x = 48 + 45

17x = 93

⇒ x = 93/17.

Substitute the x  value in equation (3).

y = 15 - 3(93/17)/4

⇒ y  = - 6/17.

Solution x  = 93/17, y  = - 6/17.

Elimination method :

Given  equations are

2x - 3y  = 12  ---> (1)

3x + 4y = 15  ---> (2)

Multiply 3 to (1) and multiply 2 to (2).

2x - 3y  = 12  ---> (1) * 3

3x + 4y = 15  ---> (2) * 2

Then the equations are,

6x - 9y  = 36  ---> (3)

6x + 8y = 30  ---> (4)

Subtract (3) from (4).

6x - 9y  = 36

6x + 8y = 30

-    +     -

__________

17y = - 6

⇒ y  = - 6/17.

Substitute the y value in equation (3).

6x - 9(- 6/17)  = 36

6x + 54/17  = 36

6x = 36 - 54/17

6x = (612 - 54)/17

6x = 558/17

x = 558/102 = 93/17

⇒ x = 93/17.

Solution x  = 93/17, y  = - 6/17.