Question

solving a system represented in a table
the tables represent two linear functions. the equation represented by the first table is given below.
y = 5.75x + 34.5
what linear equation is represented by the second table?
y = -2.5x - 15
what is the solution to the system of equations?
(-6 3, -10.75)
(-6.3, -0.75)
(-6, 0)
(0, -6)

Explanation:

Step1: Set equations equal

Set $5.75x + 34.5 = -2.5x - 15$

Step2: Combine like terms

Add $2.5x$ to both sides:
$5.75x + 2.5x + 34.5 = -15$
$8.25x + 34.5 = -15$

Step3: Isolate x term

Subtract 34.5 from both sides:
$8.25x = -15 - 34.5$
$8.25x = -49.5$

Step4: Solve for x

$x = \frac{-49.5}{8.25} = -6$

Step5: Find y with x=-6

Substitute $x=-6$ into $y=-2.5x -15$:
$y = -2.5(-6) -15 = 15 -15 = 0$

Answer:

$(-6, 0)$