Question

1. determine which ordered pairs are a solution to this system of equations.

(-4, -5) (-2, -4.5) (0, 1)
$y = \frac{1}{4}x - 4$
$y = 2.75x + 1$

Explanation:

Step1: Test (-4, -5)

Substitute \( x = -4 \), \( y = -5 \) into \( y = \frac{1}{4}x - 4 \):
\( \frac{1}{4}(-4) - 4 = -1 - 4 = -5 \).
Substitute into \( y = 2.75x + 1 \):
\( 2.75(-4) + 1 = -11 + 1 = -10
eq -5 \).
Not a solution.

Step2: Test (-2, -4.5)

Substitute \( x = -2 \), \( y = -4.5 \) into \( y = \frac{1}{4}x - 4 \):
\( \frac{1}{4}(-2) - 4 = -0.5 - 4 = -4.5 \).
Substitute into \( y = 2.75x + 1 \):
\( 2.75(-2) + 1 = -5.5 + 1 = -4.5 \).
Satisfies both equations.

Step3: Test (0, 1)

Substitute \( x = 0 \), \( y = 1 \) into \( y = \frac{1}{4}x - 4 \):
\( \frac{1}{4}(0) - 4 = -4
eq 1 \).
Not a solution.

Answer:

\((-2, -4.5)\)