Question

what is the solution to the system of equations below?
y = -\frac{1}{4}x + 2 and 3y = -\frac{3}{4}x - 6
\bigcirc no solution
\bigcirc infinitely many solutions
\bigcirc (-16, 6)
\bigcirc (-16, -2)

Explanation:

Step1: Simplify the second equation

Divide the second equation \(3y = -\frac{3}{4}x - 6\) by 3. We get \(y = -\frac{1}{4}x - 2\).

Step2: Compare the two equations

The first equation is \(y = -\frac{1}{4}x + 2\) and the simplified second equation is \(y = -\frac{1}{4}x - 2\). The slopes (\(-\frac{1}{4}\)) are the same, but the y - intercepts (2 and - 2) are different. When two linear equations have the same slope and different y - intercepts, they are parallel lines and do not intersect. So, there is no solution for this system of equations.

Answer:

no solution