How do you solve the system of equations 3x - 6y = - 9 and - 6x + 10y = 6?

1 Answer
Jun 2, 2017

refer below.

Explanation:

Solve the equations simultaneously.

Firstly, choose 1 equation and make either x or y the subject.

3x-6y=-9

3x=-9+6y

color(red)x=-3+2y ------- (1) Let this be equation 1.

-6color(red)x+10y=6 ------(2) Let this be equation 2.

Notice both equations have x?

Substitute (1) into (2).

-6(-3+2y)+10y=6
The x has been eliminated, and y can now be found.

18-12y+10y=6

-12y+10y=6-18

-2y=-12

color(blue)(y=6)

Since y=6, we can substitute this y value into (1).

x=-3+2(6)

color(red)(x=9)

When the x and y values are found, be sure to double check whether the answers satisfy the original equations.

When y=6 and x=9,

3x-6y=-9

3(9) - 6(6) = -9

27-36=-9

-9=-9

Since both sides of the equation match, the answers are correct.