Question

1. $y=\frac{1}{3}x-3$

$y=-x+1$

Explanation:

Step1: Set equations equal to each other

$\frac{1}{3}x - 3 = -x + 1$

Step2: Multiply by 3 to eliminate fraction

$x - 9 = -3x + 3$

Step3: Combine like terms for x

$x + 3x = 3 + 9$
$4x = 12$

Step4: Solve for x

$x = \frac{12}{4} = 3$

Step5: Substitute x to find y

$y = -(3) + 1 = -2$

Answer:

The solution to the system is $(3, -2)$

To graph the lines:

1. For $y=\frac{1}{3}x - 3$: plot the y-intercept $(0, -3)$, then use slope $\frac{1}{3}$ (rise 1, run 3) to find another point like $(3, -2)$.
2. For $y=-x + 1$: plot the y-intercept $(0, 1)$, then use slope $-1$ (rise -1, run 1) to find another point like $(3, -2)$.

The two lines intersect at $(3, -2)$.