Use the table to answer the question.

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

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

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

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

There is no solution.

Answer 1

To find the solution to the system of equations represented in Jian's table, we need to identify points where the y-values from both equations are equal for the same x-value.

The equations given are:

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

From the table, we can see the y-values for each x-value:

For \( x = 0 \):

• \( y = 2(0) - 5 = -5 \)
• \( y = 0 - 3 = -3 \)

For \( x = 1 \):

• \( y = 2(1) - 5 = -3 \)
• \( y = 1 - 3 = -2 \)

For \( x = 2 \):

• \( y = 2(2) - 5 = -1 \)
• \( y = 2 - 3 = -1 \)

For \( x = 3 \):

• \( y = 2(3) - 5 = 1 \)
• \( y = 3 - 3 = 0 \)

Now, let's look for points where the y-values are the same:

• At \( x = 2 \), both equations yield \( y = -1 \).

This means the point \( (2, -1) \) is where both equations intersect, indicating it is the solution to the system of equations.

Thus, the correct response is: (2, −1)