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____ [38]
2 years ago
11

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 tab

le. What is the solution to the system of equations​

Social Studies
1 answer:
fomenos2 years ago
7 0

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)

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