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.