Question

1. math on the spot use a separate sheet of graph paper to solve each system by graphing. check your answer. a. \\(\

$$\begin{cases} y = x + 2 \\\\ y = -2x + 5 \\end{cases}$$

\\) \\(\underline{\quad\quad\quad\quad}\\) b. \\(\

$$\begin{cases} x - y = 2 \\\\ y = \\frac{1}{2}x \\end{cases}$$

\\) \\(\underline{\quad\quad\quad\quad}\\) module 7 • lesson 2

Explanation:

Step1: Set equations equal (Part A)

Since $y = x + 2$ and $y = -2x + 5$, set $x + 2 = -2x + 5$.

Step2: Solve for x (Part A)

$x + 2x = 5 - 2$
$3x = 3$
$x = 1$

Step3: Find y (Part A)

Substitute $x=1$ into $y = x + 2$:
$y = 1 + 2 = 3$

Step4: Rewrite first equation (Part B)

Rewrite $x - y = 2$ as $y = x - 2$.

Step5: Set equations equal (Part B)

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

Step6: Solve for x (Part B)

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

Step7: Find y (Part B)

Substitute $x=4$ into $y = \frac{1}{2}x$:
$y = \frac{1}{2}(4) = 2$

Answer:

A. $(1, 3)$
B. $(4, 2)$