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)