Question

solve the system of linear equations by graphing.
y = -\frac{1}{2}x + 3
y = \frac{1}{2}x - 2
\left(\frac{1}{2}, -5\
ight)
\left(\frac{1}{2}, 5\
ight)
\left(5, \frac{1}{2}\
ight)
\left(-5, \frac{1}{2}\
ight)

Explanation:

Step1: Set equations equal

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

Step2: Isolate x terms

$$3 + 2 = \frac{1}{2}x + \frac{1}{2}x$$
$$5 = x$$

Step3: Substitute x to find y

$$y = -\frac{1}{2}(5) + 3$$
$$y = -\frac{5}{2} + \frac{6}{2} = \frac{1}{2}$$

Answer:

$\boldsymbol{(5, \frac{1}{2})}$