solving a system of linear equations by graphing\nsolve this system of linear equations:\n$4x - 2y = 8$\n$y…

Explanation:

Step1: Find x-intercept of $4x-2y=8$

Set $y=0$, solve for $x$: $4x - 2(0) = 8$ $4x = 8$ $x = \frac{8}{4} = 2$

Step2: Identify intercept coordinate

The x-intercept is the point where $y=0$, so the coordinate is $(2, 0)$.

Step3: Verify second line's intercept (optional check)

For $y=\frac{1}{2}x-2$, set $y=0$: $0=\frac{1}{2}x-2$ $\frac{1}{2}x=2$ $x=4$, so its x-intercept is $(4,0)$

Step4: Find intersection (full solution)

Substitute $y=\frac{1}{2}x-2$ into $4x-2y=8$: $4x - 2\left(\frac{1}{2}x - 2\right) = 8$ $4x - x + 4 = 8$ $3x = 4$ $x=\frac{4}{3}$ Then $y=\frac{1}{2}\left(\frac{4}{3}\right)-2=\frac{2}{3}-2=-\frac{4}{3}$

Answer:

1. The x-intercept of the first equation $4x-2y=8$ is the point $\boldsymbol{(2, 0)}$ (to plot on the graph).
2. The solution to the system of equations is $\boldsymbol{x=\frac{4}{3}, y=-\frac{4}{3}}$ or the point $\boldsymbol{\left(\frac{4}{3}, -\frac{4}{3}\right)}$