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 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

(3,0)

Answer 1

To find the solution for the system of equations given in the table, we need to look for a point where the y-values for both equations are equal for the same x-value.

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 \( x = 3 \):

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

The only point where the y-values for both equations are equal is at \( (2, -1) \).

Therefore, the solution for the system of equations is \( \boxed{(2, -1)} \).