Question

Solve the system of equations.6x−3y=−6 9x−3y=−18

Answer 1

Solve the system of equations.5x–4y=–44 –x+3y=22

Answer 2

To solve the system of equations, we can use the method of elimination. We want to eliminate the variable "y".

First, we can multiply the first equation by 3:

(3)(6x - 3y) = (3)(-6)
18x - 9y = -18

Now, we can subtract the second equation from the first equation:

(18x - 9y) - (9x - 3y) = (-18) - (-18)
18x - 9y - 9x + 3y = -18 + 18
9x - 6y = 0

Simplifying further, we have:

3x - 2y = 0

Now we have a new system of equations:

9x - 3y = -18
3x - 2y = 0

To eliminate the variable "y", we can multiply the second equation by 3:

(3)(3x - 2y) = (3)(0)
9x - 6y = 0

Now we can subtract this equation from the first equation:

(9x - 3y) - (9x - 6y) = (-18) - (0)
9x - 3y - 9x + 6y = -18
3y - 6y = -18
-3y = -18

Dividing both sides by -3, we get:

y = 6

Substituting this value of y into any of the original equations, we can solve for x. Let's use the first equation:

6x - 3(6) = -6
6x - 18 = -6
6x = 12
x = 2

Therefore, the solution to the system of equations is x = 2 and y = 6.