Question

xjavascript:void(0)-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

(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.

(2,−1)

Answer 1

To identify the solution for the system of equations given in Jian's table, we need to analyze the two equations:

1. \( y = 2x - 5 \)
2. \( y = x - 3 \)

We can determine the solution to the system by finding the point (x, y) where both equations give the same y-value.

From the table, we can observe the y-values for different x-values:

- At \( x = 0 \): \( y = -5 \) (from both equations)
- At \( x = 1 \): \( y = -3 \) (from both equations)
- At \( x = 2 \): \( y = -1 \) (from both equations)
- At \( x = 3 \): \( y = 1 \) for the first equation and \( y = 0 \) for the second equation

Now, checking these values, we see they only match at:

- \( x = 2 \): \( y = -1 \) (this is in both equations)

We can also evaluate the equations to find the intersection point analytically by setting them equal to each other:

\[
2x - 5 = x - 3
\]
\[
2x - x = -3 + 5
\]
\[
x = 2
\]

Now substituting \( x = 2 \) back into either equation to find \( y \):
\[
y = 2(2) - 5 = 4 - 5 = -1
\]

Thus, the solution to the system of equations is:

\((2, -1)\)

So the correct answer is:

**(2, −1)**