Question

graph these equations:
-2y = -x + 6
2y = x - 6
click to select points on the graph.
graph with x-axis from -10 to 10 and y-axis from -10 to 10
-2y = -x + 6 (green button)
2y = x - 6 (purple button)
how many solutions does the system of equations have?

Explanation:

Step1: Rewrite first equation to slope-intercept form

Divide both sides by $-2$:
$$y = \frac{1}{2}x - 3$$

Step2: Rewrite second equation to slope-intercept form

Divide both sides by $2$:
$$y = \frac{1}{2}x - 3$$

Step3: Analyze the two equations

Both equations simplify to the same linear equation, meaning they represent the exact same line on the graph. Every point on this line is a solution to the system.

Step4: Identify key points for graphing

• When $x=0$: $y = \frac{1}{2}(0) - 3 = -3$, so the point is $(0, -3)$
• When $y=0$: $0 = \frac{1}{2}x - 3 \implies x=6$, so the point is $(6, 0)$

Answer:

The two equations graph as the same line. The system has infinitely many solutions.
Key points to plot for the line: $(0, -3)$ and $(6, 0)$ (all points along this line satisfy both equations).