Question

solve the system of equation 6x - 3y = -6, 9x - 3y = -18

Answer 1

To solve this system of equations, we will use the method of substitution or elimination.

1. Using substitution method:
From the first equation:
6x - 3y = -6
Rearranging the equation:
y = 2x + 2

Now substitute this value of y into the second equation:
9x - 3(2x + 2) = -18
Simplify:
9x - 6x - 6 = -18
3x - 6 = -18
3x = -12
x = -4

Now substitute the value of x back into the equation y = 2x + 2:
y = 2(-4) + 2
y = -8 + 2
y = -6

Therefore, the solution to the system of equations is x = -4 and y = -6.

2. Using elimination method:
Multiply the first equation by 3 and the second equation by 2 to make the coefficients of y the same:
(1) 18x - 9y = -18
(2) 18x - 6y = -36

Subtract equation (1) from equation (2) to eliminate x:
18x - 6y - (18x - 9y) = -36 - (-18)
18x - 6y - 18x + 9y = -36 + 18
3y = -18
y = -6

Now substitute the value of y back into the first equation:
6x - 3(-6) = -6
6x + 18 = -6
6x = -24
x = -4

Therefore, the solution to the system of equations is x = -4 and y = -6.