Solve the simultaneous equations

3x - 4y = 18

9x + 2y = 12

x = 2 and y = - 3

Step-by-step explanation:

Multiply the first equation by 3 to make the x coefficients the same for both equations.

It becomes 9x - 12y = 54. (eqn 1)

and 9x + 2y = 12 (eqn 2)

subtract eqn 2 from eqn 1

9x - 9x - 12y - 2y = 54 - 12

-14y = 42

dividing both sides by - 14

y = - 3

Substituting y as - 3 in eqn 1

9x - 12 (-3) = 54

9x + 36 = 54

9x = 54 - 36

9x = 18

dividing both sides by 9

x = 2

3x - 4y = 18

9x + 2y = 12

Solve for x in the first equation.

3x - 4y = 18

3x = 18 + 4y

x = (18 + 4y) / 3

x = 6+4/3y

Put x as 6+4/3y in the second equation and solve for y.

9x + 2y = 12

9 (6+4/3y) + 2y = 12

12y+54+2y=12

14y+54=12

14y=12-54

14y=-42

y = - 3

Put y as - 3 in the first equation to solve for x.

3x - 4y = 18

3x - 4 (-3) = 18

3x+12=18

3x=18-12

3x=6

x = 2