solve the following system of equations graphically on the set of axes below.\n$y = \\frac{1}{3}x + 8$\n$x +…

Explanation:

Step1: Rewrite the second - equation in slope - intercept form

For $x + y=4$, we can rewrite it as $y=-x + 4$. The slope $m=-1$ and the $y$ - intercept $b = 4$.

Step2: Identify key points for the first line $y=\frac{1}{3}x + 8$

When $x = 0$, $y=\frac{1}{3}(0)+8=8$, so one point is $(0,8)$. When $y = 0$, $0=\frac{1}{3}x+8$, then $\frac{1}{3}x=-8$, and $x=-24$.

Step3: Identify key points for the second line $y=-x + 4$

When $x = 0$, $y=4$, so one point is $(0,4)$. When $y = 0$, $0=-x + 4$, then $x = 4$.

Step4: Find the intersection point

Set $\frac{1}{3}x+8=-x + 4$. Add $x$ to both sides: $\frac{1}{3}x+x+8=-x+x + 4$, which simplifies to $\frac{1}{3}x+\frac{3}{3}x+8=4$, or $\frac{4}{3}x+8=4$. Subtract 8 from both sides: $\frac{4}{3}x+8 - 8=4 - 8$, so $\frac{4}{3}x=-4$. Multiply both sides by $\frac{3}{4}$: $x=-4\times\frac{3}{4}=-3$. Substitute $x=-3$ into $y=-x + 4$, we get $y=-(-3)+4=7$.

Answer:

$x=-3,y = 7$