solve the following system of equations graphically on the set of axes below.$y = x - 5$$y = -\frac{1}{2}x +…

Explanation:

Step1: Find intercepts for $y=x-5$

For x-intercept: set $y=0$: $0 = x - 5 \implies x=5$, so point $(5, 0)$ For y-intercept: set $x=0$: $y=0-5=-5$, so point $(0, -5)$

Step2: Find intercepts for $y=-\frac{1}{2}x+7$

For x-intercept: set $y=0$: $0 = -\frac{1}{2}x + 7 \implies \frac{1}{2}x=7 \implies x=14$, so point $(14, 0)$ For y-intercept: set $x=0$: $y=0+7=7$, so point $(0, 7)$

Step3: Solve algebraically to find intersection

Set equations equal: $x - 5 = -\frac{1}{2}x + 7$ Add $\frac{1}{2}x$ to both sides: $\frac{3}{2}x - 5 = 7$ Add 5 to both sides: $\frac{3}{2}x = 12$ Multiply by $\frac{2}{3}$: $x = 12 \times \frac{2}{3} = 8$ Substitute $x=8$ into $y=x-5$: $y=8-5=3$

Answer:

The intersection point (solution) is $(8, 3)$. To plot the lines:

1. For $y=x-5$: plot $(5, 0)$ and $(0, -5)$, draw a line through them.
2. For $y=-\frac{1}{2}x+7$: plot $(14, 0)$ and $(0, 7)$, draw a line through them. The lines cross at $(8, 3)$.