use process of elimination: 3x+3y=0 and minus, 7, x, minus, 9, y, equals, 18−7x−9y=18

1 answer

To use the process of elimination to solve the given system of equations, we can eliminate one variable at a time by adding or subtracting the equations.

First, we can eliminate the variable "x" by subtracting the two equations:

(3x + 3y) - (18 - 7x - 9y) = 0 - 18
3x + 3y - 18 + 7x + 9y = -18
10x + 12y = 0

Now we have one equation with only the variable "y" remaining.

Next, we can eliminate the variable "y" by adding the two equations:

(10x + 12y) + (18 - 7x - 9y) = 0 + 18
10x + 12y + 18 - 7x - 9y = 18
3x + 3y + 18 = 18
3x + 3y = 0

We can observe that the equation "3x + 3y = 0" is same as the first equation "3x + 3y = 0". Therefore, the system of equations is dependent and has infinitely many solutions.