Question

graph the system below and write its solution.\

$$\begin{cases}-2x + y = -4 \\\\ y = \\dfrac{1}{3}x + 1\\end{cases}$$

\
note that you can also answer
o solution\ or \infinitely many\ solutions.\
solution: \square

Explanation:

Step1: Rewrite first equation to slope-intercept

$y=2x-4$

Step2: Set equations equal to each other

$2x-4=\frac{1}{3}x+1$

Step3: Solve for x

Multiply all terms by 3: $6x-12=x+3$
Subtract $x$: $5x-12=3$
Add 12: $5x=15$
Divide by 5: $x=3$

Step4: Find y with x=3

$y=2(3)-4=6-4=2$

Step5: Verify with second equation

$y=\frac{1}{3}(3)+1=1+1=2$

Answer:

$(3, 2)$

To graph:

1. For $y=2x-4$: plot y-intercept $(0,-4)$, use slope 2 to plot $(1,-2)$, draw the line.
2. For $y=\frac{1}{3}x+1$: plot y-intercept $(0,1)$, use slope $\frac{1}{3}$ to plot $(3,2)$, draw the line.

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