Use the table to answer the question.

Question

x-value y-value if y=2x−5
y
=
2
x
−
5
y-value if y=x−3
y
=
x
−
3
0 −5
−
5
−3
−
3
1 −3
−
3
−2
−
2
2 −1
−
1
−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)
(
3
,
0
)
left parenthesis 3 comma 0 right parenthesis

There is no solution.
There is no solution.

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

There is an infinite number of solutions.

Answer 1

To identify the solution for the system of equations, we need to find the point that satisfies both equations:

1. y = 2x - 5
2. y = x - 3

From the table data provided, we can see the y-values corresponding to the x-values for both equations:

• For x = 3:

  • From y = 2x - 5: y = 2(3) - 5 = 6 - 5 = 1
  • From y = x - 3: y = 3 - 3 = 0

• For x = 2:

  • From y = 2x - 5: y = 2(2) - 5 = 4 - 5 = -1
  • From y = x - 3: y = 2 - 3 = -1

• For x = 1:

  • From y = 2x - 5: y = 2(1) - 5 = 2 - 5 = -3
  • From y = x - 3: y = 1 - 3 = -2

• For x = 0:

  • From y = 2x - 5: y = 2(0) - 5 = -5
  • From y = x - 3: y = 0 - 3 = -3

• For x = -1:

  • From y = 2x - 5: y = 2(-1) - 5 = -2 - 5 = -7
  • From y = x - 3: y = -1 - 3 = -4

• For x = -2:

  • From y = 2x - 5: y = 2(-2) - 5 = -4 - 5 = -9
  • From y = x - 3: y = -2 - 3 = -5

The point that satisfies both equations is (2, -1) since for x = 2, both equations yield y = -1.

Thus, the correct response is:

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