What is the solution to the system of equations below?
y = negative one-third x + 6 and y = one-third x minus 6
no solution
infinitely many solutions
(–18, 12)
(18, 0)
(18, 0)
To find the solution to the system of equations, we need to find the point where both equations intersect.
The two equations given are:
y = -1/3x + 6 (equation 1)
y = 1/3x - 6 (equation 2)
By setting the two equations equal to each other, we can find the x-coordinate:
-1/3x + 6 = 1/3x - 6
First, we can simplify both sides of the equation by adding 1/3x to both sides:
6 + 1/3x = 6 + 1/3x
Next, by subtracting 6 from both sides, we get:
1/3x - 1/3x = -6 - 6
This simplifies to:
0 = -12
Since 0 does not equal -12, this means there is no solution to the system of equations. Therefore, the correct answer is no solution.