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

There is no solution.
There is no solution.

(2,−1)

Answer 1

To find the solution for the system of equations represented in Jian's table, we need to look for a pair of (x, y) values that satisfy both equations:

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

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 \( x = 3 \):

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

Looking at the results, the only point where the y-values from both equations are equal in the table is at \( (2, -1) \).

Thus, the solution for the system of equations is:

(2, −1).