Question

Use the table to answer the 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

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

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

There is an infinite number of solutions.
There is an infinite number of solutions.

There is no solution.
There is no solution.
Skip to navigation

Answer 1

To find the solution for the given system of equations using Jian's table, we need to look for the point where both equations yield the same y-value for the same x-value.

From the table:

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 \( x = 3 \), \( y = 0 \)

Now, let's compare the y-values for the same x-values:

- For \( x = 0 \): \( y = -5 \) (from \( y = 2x - 5 \)) and \( y = -3 \) (from \( y = x - 3 \)) → Not a solution
- For \( x = 1 \): \( y = -3 \) and \( y = -2 \) → Not a solution
- For \( x = 2 \): \( y = -1 \) and \( y = -1 \) → **This is a solution: (2, -1)**
- For \( x = 3 \): \( y = 1 \) and \( y = 0 \) → Not a solution

Thus, the solution to the system represented by Jian's table is:
**(2, -1)**

So, the correct response is:
**(2, −1)**