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

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

There is no solution.
There is no solution.

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

(2,−1)

Answer 1

To identify the solution for the system of equations given the two equations \( y = 2x - 5 \) and \( y = x - 3 \), we need to find the values of \( x \) where both equations yield the same \( y \)-value.

From Jian's table:

• For \( x = 0 \), \( y = -5 \) from the first equation and \( y = -3 \) from the second equation (not a solution).
• For \( x = 1 \), \( y = -3 \) from the first equation and \( y = -2 \) from the second equation (not a solution).
• For \( x = 2 \), \( y = -1 \) from the first equation and \( y = -1 \) from the second equation (this is a solution).
• For \( x = 3 \), \( y = 1 \) from the first equation and \( y = 0 \) from the second equation (not a solution).

The only point where both equations have the same \( y \)-value is at \( (2, -1) \).

Thus, the solution for the system is:

(2, −1)