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

(2,−1)
(
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.
There is an infinite number of solutions.

(3,0)

Answer 1

To identify the solution for the system of equations given by the two lines, we should find the point where the two equations intersect.

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

For \( y = 2x - 5 \):

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

For \( y = x - 3 \):

• \( x = 0 \): \( y = -3 \)
• \( x = 1 \): \( y = -2 \)
• \( x = 2 \): \( y = -1 \)
• \( x = 3 \): \( y = 0 \)

Now, let’s find the common (x, y) values in both equations:

For \( x = 2 \):

• The y-value for \( y = 2x - 5 \) is \( -1 \).
• The y-value for \( y = x - 3 \) is also \( -1 \).

Since both equations give the same output when \( x = 2 \), the point (2, -1) is a solution to the system of equations.

Thus, the answer is:

\( (2, -1) \)