Question

how many solutions does the system have?\

$$\begin{cases}y = -3x + 9\\\\3y = -9x + 9\\end{cases}$$

choose 1 answer:\
a exactly one solution\
b no solutions\
c infinitely many solutions

Explanation:

Step1: Simplify the second equation

Divide the second equation \(3y = -9x + 9\) by 3: \(y = -3x + 3\).

Step2: Compare with the first equation

The first equation is \(y = -3x + 9\). The slopes (\(-3\)) are equal, but the y - intercepts (9 vs. 3) are different. Parallel lines (same slope, different y - intercepts) never intersect, so the system has no solutions.

Answer:

B. No solutions