Question

solve by graphing.
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$$\begin{cases} y = \\frac{1}{2}x + 1 \\\\ y = -x + 4 \\end{cases}$$

(\boxed{?}, \boxed{})

Explanation:

Step1: Find intersection by solving equations

Set the two equations equal: $\frac{1}{2}x + 1 = -x + 4$

Step2: Solve for x

Add $x$ to both sides: $\frac{1}{2}x + x + 1 = 4$
Combine like terms: $\frac{3}{2}x + 1 = 4$
Subtract 1: $\frac{3}{2}x = 3$
Multiply by $\frac{2}{3}$: $x = 2$

Step3: Find y using x=2

Substitute x=2 into $y = -x + 4$: $y = -2 + 4 = 2$

Answer:

(2, 2)