Question

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.

Table:

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

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Answers (with radio buttons):

(3, 0)
There is no solution.
There is an infinite number of solutions.
(2, -1)

Answer 1

To find the solution for the system of equations represented by Jian's table, we need to look for the x-value where the y-values from both equations are equal.

The equations given are:
1. \( y = 2x - 5 \)
2. \( y = x - 3 \)

Let's analyze the table provided:

| 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 |

Now we compare the y-values from both equations:

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

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

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

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

We see that at \( x = 2 \), both equations yield the same y-value of -1. Therefore, the solution to the system of equations is:
\[
(2, -1)
\]

### So, the correct answer is:
(2, -1)