Question 2 (Worth 3 points)

(02.02 LC)

The equations x + y = 3 and y equals the quantity x minus 5 end quantity over the quantity x minus 3 end quantity are represented in the graph.

Rational function with one piece that increases from the left in quadrant 2 asymptotic to the line y equals 1 passing through the point 1 comma 2 and then increasing asymptotic to the line x equals 3 and another piece that increases from the left in quadrant 4 asymptotic to the line x equals 3 passing through the point 4 comma negative 1 and then increasing asymptotic to the line y equals 1 and a linear function decreasing from the left in quadrant 2 passing through the point 0 comma 3 and 1 comma 2 and 4 comma negative 1.

Determine the solution(s) to the system of equations.

(−1, −2) and (4, −1)

(−1, −2) and (−4, −1)

(1, 2) and (4, −1)

(1, 2) and (−4, −1)

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semsee45 semsee45 · Answer 1 · 2024-01-23T19:05:53+01:00

Answer:

D) (1, 2) and (-4, -1)

Step-by-step explanation:

The following equations are represented in the attached graph:

[tex]\textsf{Equation 1:}\quad x + y = 3[/tex]

[tex]\textsf{Equation 2:}\quad y = \dfrac{x-5}{x-3}[/tex]

The solutions to the system of equations are the points of intersection of the two graphed equations.

Upon observation of the graph, the points of intersection are:

[tex]\Large\boxed{\boxed{(1, 2)\;\;\textsf{and}\;\;(-4, -1)}}[/tex]

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