Answer:
C. (2, -2)
Explanation:
Given:
[tex] y = \frac{1}{2}x - 3 [/tex] ----› Equation 1
Use the table to generate equation two of the system.
First, find the slope (m), and y-intercept (b).
Using two pairs, (0, 0) and (2, -2),
[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-2 - 0}{2 - 0} = \frac{-2}{2} = -1 [/tex]
y-intercept (b) = 0 (i.e the value of y when x = 0)
Substitute m = -1, and b = 0 in [tex] y = mx + b [/tex]
Thus:
[tex] y = (-1)(x) + 0 [/tex]
[tex] y = -x [/tex] ----› Equation 2.
✔️Solve for x by substituting y = -x in equation 1
[tex] y = \frac{1}{2}x - 3 [/tex]
[tex] -x = \frac{1}{2}x - 3 [/tex]
Add 3 to both sides
[tex] -x + 3 = \frac{1}{2}x - 3 + 3 [/tex]
[tex] -x + 3 = \frac{1}{2}x [/tex]
Multiply both sides by 2
[tex] (-x + 3) \times 2 = \frac{1}{2}x \times 2 [/tex]
[tex] -2x + 6 = x [/tex]
Collect like terms
[tex] -2x - x = -6 [/tex]
[tex] -3x = -6 [/tex]
Divide both sides by -3
[tex] x = 2 [/tex]
✔️Substitute x = 2 in equation 2.
[tex] y = -x [/tex]
[tex] y = -2 [/tex]
Therefore the solution to the system of equations would be:
(2, -2)
