Question

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how many solutions does the system of equations below have?
$x - y=-3$
$2x - 2y=-6$
no solution
one solution
infinitely many solutions

Explanation:

Step1: Simplify the second equation

Divide the second - equation $2x - 2y=-6$ by 2. We get $\frac{2x}{2}-\frac{2y}{2}=\frac{-6}{2}$, which simplifies to $x - y=-3$.

Step2: Analyze the relationship between the equations

The first equation is $x - y=-3$ and the simplified second equation is also $x - y=-3$. Since the two equations are identical, they represent the same line.

Answer:

infinitely many solutions