Question

9x - 6y = -21 and 6x - 12y = -6 How would I solve by substitution?

Answer 1

x = -3 ; y = -1

Explanation:

Let 9x - 6y = -21 be eqn.1 & let 6x - 12y = -6 be eqn.2 .

Lets find the value of x from eqn.1

`9x - 6y= -21`

`=> 3(3x - 2y) = -21`

`=> 3x - 2y = (-21)/(3) = -7`

`=> x = (2y - 7)/(3)`

Now , lets put the value of x (which we got from eqn.1) in eqn.2 :-

`6x - 12y = -6`

`=> 6(x - 2y) = -6`

`=> x - 2y = (-6)/(6) = -1`

(Putting x here)

`=> (2y - 7)/(3) - 2y = -1`

`=> (2y - 7 - 6x)/(3) = - 1`

`=> -4 y - 7 = -1 * 3 = -3`

`=> -4y = 7 - 3 = 4`

`=> y = (-4)/(4) = -1`

Now , lets find the value of x.

`x = (2y - 7)/(3)`

Putting y = -0.5 gives ,

`x = ([2 * (-1)] - 7)/(3)`

`=> x = (-2 - 7)/(3) = (-9)/(3) = -3`

Answer 2

(-3,-1)

Explanation:

6x-12y=-6

6x=12y-6

x=2y-1

9(2y-1)-6y= -21

18y-9-6y=-21

12y= -12

y=-1

6x-12(-1)=-6

6x+12= -6

6x=-18

x=-3