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.

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

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

There is an infinite number of solutions.

Answer 1

To find the solution to the system of equations, we need to identify the point at which the two equations intersect. Let’s look at the y-values from the table for each corresponding x-value:

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

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

For the equation \( y = x - 3 \):

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

Next, we find a common (x, y) pair from both equations. From the table:

• At \( x = 2 \), the \( y \) value for both equations is \( -1 \).
• At \( x = 3 \), the \( y \) value for \( y = 2x - 5 \) is \( 1 \) and for \( y = x - 3 \) is \( 0 \).

The only solution that satisfies both equations is when \( x = 2 \) and \( y = -1 \).

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

The correct response is:

(2,−1)