graph the system below and write its solution.\n$\begin{cases}y = \frac{1}{2}x + 2\\-3x + y=-3end{cases}$\nno…

Explanation:

Step1: Rewrite the second - equation in slope - intercept form ($y=mx + b$)

Starting with $-3x + y=-3$, add $3x$ to both sides. We get $y = 3x-3$.

Step2: Set the two equations equal to each other

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

Step3: Solve for $x$

First, subtract $\frac{1}{2}x$ from both sides: $2=3x-\frac{1}{2}x - 3$. Combine like terms: $2=\frac{6x - x}{2}-3$, so $2=\frac{5x}{2}-3$. Add 3 to both sides: $2 + 3=\frac{5x}{2}$, which gives $5=\frac{5x}{2}$. Multiply both sides by $\frac{2}{5}$: $x = 2$.

Step4: Solve for $y$

Substitute $x = 2$ into the first equation $y=\frac{1}{2}x+2$. Then $y=\frac{1}{2}\times2+2=1 + 2=3$.

Answer:

$(2,3)$