The question is incomplete! Complete question along with answer and step by step explanation is provided below.
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:
The solution is
[tex](x, y) = (2,67, -4.33)[/tex]
Therefore, the correct statement is
The x-value is between 2 and 3, and the y-value is between –4 and –5.
Step-by-step explanation:
The given equations are
Equation 1:
[tex]y = \frac{1}{4}x - 5[/tex]
Equation 2:
[tex]y = -\frac{1}{2}x - 3[/tex]
The point of intersection is given by
[tex]\frac{1}{4}x - 5 = -\frac{1}{2}x - 3 \\\\\frac{1}{4}x + \frac{1}{2}x = 5 - 3 \\\\\frac{3}{4}x = 2 \\\\x = \frac{2 (4)}{3} \\\\x = \frac{8}{3} \\\\x = 2.67[/tex]
The corresponding y value is
[tex]y = \frac{1}{4}x - 5 \\\\y = \frac{1}{4}(\frac{8}{3}) - 5 \\\\y = \frac{2}{3} - 5 \\\\y = -\frac{13}{3} \\\\y = -4.33[/tex]
So the solution is
[tex](x, y) = (2,67, -4.33)[/tex]
Therefore, the correct statement is
The x-value is between 2 and 3, and the y-value is between –4 and –5.
Answer: This question doesn't give the the answer choices or show the graph. So this question is incomplete
Step-by-step explanation:
