Question

The system of equations y = one-fourth x minus 5 and y = negative one-half x minus 3 is shown on the graph below. Which statement is true about the solution to the system of equations? The x-value is between 2 and 3, and the y-value is between –4 and –5. The x-value is between –4 and –5, and the y-value is between 2 and 3. The x-value is between –2 and –3, and the y-value is between 4 and 5. The x-value is between 4 and 5, and the y-value is between –2 and –3.

Answer 1

A: The x-value is between 2 and 3, and the y-value is between –4 and –5.

Explanation:

Answer 2

The x-value is between 2 and 3, and the y-value is between –4 and –5.

Explanation:

The system of equations y = (1/4)x - 5 and y = -(1/2)x - 3.

The solution of the equation is the point of intersection of the two lines, from the graph, the intersection of the red and blue lines which represent the equation of the lines has an x-value is between 2 and 3, and the y-value is between –4 and –5.

Also the solution of the equation can be solved by solving the two equations simultaneously:

y = (1/4)x - 5 . . . 1)

y = -(1/2)x - 3 . . . 2)

Subtracting equation 2 from 1:

0 = (3/4)x - 2

(3/4)x = 2

x = 2 × 4/3

x = 8/3 = 2.67

x = 2.67

To find y put x = 2.67 in equation 1:

y = (1/4)(8/3) - 5

y = 8/12 - 5

y = -13/3

y = -4.33