Question

question 1 given is a system of equations, $y = \frac{1}{2}x - 3$ $x - 2y = 6$ how many solutions are there? \bigcirc one solution \bigcirc two solutions \bigcirc infinitely many solutions \bigcirc no solution

Explanation:

Step1: Rearrange second equation

Solve $x-2y=6$ for $y$:
Subtract $x$ from both sides: $-2y = -x + 6$
Divide by $-2$: $y = \frac{1}{2}x - 3$

Step2: Compare the two equations

The first equation is $y = \frac{1}{2}x - 3$, which matches the rearranged second equation. This means the two equations represent the same line, so every point on the line is a solution.

Answer:

Infinitely many solutions