Question

the graph below represents the liner equation y equals 1 and 1/2 x -3 A second linear equation is represented by data in the table. What is the solution to the system of equations​

Answer 1

Answer:

C. (2, -2)

Explanation:

Given:

$y = \frac{1}{2}x - 3$ ----› 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),

$slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-2 - 0}{2 - 0} = \frac{-2}{2} = -1$

y-intercept (b) = 0 (i.e  the value of y when x = 0)

Substitute m = -1, and b = 0 in $y = mx + b$

Thus:

$y = (-1)(x) + 0$

$y = -x$ ----› Equation 2.

✔️Solve for x by substituting y = -x in equation 1

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

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

Add 3 to both sides

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

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

Multiply both sides by 2

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

$-2x + 6 = x$

Collect like terms

$-2x - x = -6$

$-3x = -6$

Divide both sides by -3

$x = 2$

✔️Substitute x = 2 in equation 2.

$y = -x$

$y = -2$

Therefore the solution to the system of equations would be:

(2, -2)