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.

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

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

There is no solution.

Answer 1

To identify the solution for the system of equations based on Jian's table, we need to look for the x-value(s) for which the y-values from both equations are equal.

From the table:

• 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 \( x = 3 \):

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

We see that when \( x = 2 \), both equations yield \( y = -1 \).

Therefore, the solution to the system of equations is \( (2, -1) \).

So the correct response is:

(2,−1)