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

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

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

There is no solution.
There is no solution.

There is an infinite number of solutions.

Answer 1

To identify the solution for the system of equations, we need to find the point where the two equations intersect, which means we need to look for a pair (x, y) that appears in both equations.

From the provided 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 pair (x, y) that has the same y-value for both equations is (2, -1).

Thus, the solution for the system is \((2, -1)\).

-response: (2,−1)