Solution Sets of Simultaneous Equations Quick Check

Question

3 of 53 of 5 Items

Question
Use the table to answer the question.

x-value y-value if y=2x−5 y-value if y=x−3
0 −5 −3
1 −3 −2
2 −1 −1
3 1 0
Jian made a table showing some x- and y-values in a system of equations. Use his table to identify the solution for the system.

(1 point)
Responses

(3,0)
left parenthesis 3 comma 0 right parenthesis

There is no solution.
There is no solution.

There is an infinite number of solutions.
There is an infinite number of solutions.

(2,−1)
left parenthesis 2 comma negative 1 right parenthesis
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Answer 1

To find the solution to the system of equations represented by the given table, we need to look for the values of \(x\) and \(y\) that satisfy both equations simultaneously.

The two equations are:

1. \(y = 2x - 5\)
2. \(y = x - 3\)

Let's check the given \( (x, y) \) pairs from the table:

1. \( (0, -5) \)

   • For \(y = 2(0) - 5 = -5\) and \(y = 0 - 3 = -3\): No solution.

2. \( (1, -3) \)

   • For \(y = 2(1) - 5 = -3\) and \(y = 1 - 3 = -2\): No solution.

3. \( (2, -1) \)

   • For \(y = 2(2) - 5 = -1\) and \(y = 2 - 3 = -1\): Both equate to -1. This is a solution.

4. \( (3, 1) \)

   • For \(y = 2(3) - 5 = 1\) and \(y = 3 - 3 = 0\): No solution.

5. \( (3, 0) \): This pair was not in the table, but based on the evaluation above, only \( (2, -1) \) matches both equations.

Given that only \( (2, -1) \) satisfies both equations, the correct response from the available options is:

(2,−1)