Question

Solve the system of equations.
6x−3y=−6
9x−3y=−18 (1 point)
( , )

Answer 1

To solve this system of equations, we can use the method of elimination.

First, let's multiply the first equation by 3:
18x - 9y = -18

Now, we can subtract the second equation from the first equation to eliminate the y term:
(18x - 9y) - (9x - 3y) = -18 - (-18)
18x - 9y - 9x + 3y = 0
9x - 6y = 0

To solve for x, we divide both sides of the equation by 9:
9x/9 - 6y/9 = 0/9
x - (2/3)y = 0

Now, we can plug this value of x back into the first equation to solve for y:
6x - 3y = -6
6(2/3)y - 3y = -6
(4/3)y - 3y = -6
(-5/3)y = -6

To solve for y, we can multiply both sides of the equation by -3/5:
((-5/3)y)(-3/5) = (-6)(-3/5)
y = 18/5

Now that we have the value of y, we can plug it back into the first equation to solve for x:
6x - 3(18/5) = -6
6x - (54/5) = -6
6x = -6 + 54/5
6x = -30/5 + 54/5
6x = 24/5

To solve for x, we can divide both sides of the equation by 6:
(6x)/6 = (24/5)/6
x = 4/5

So the solution to the system of equations is (x, y) = (4/5, 18/5).