Question

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

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

(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.
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Answer 1

To find the solution for the system of equations given by the two equations \( y = 2x - 5 \) and \( y = x - 3 \), we need to look for an \( (x, y) \) pair that satisfies both equations.

From Jian's table, we identify the following points (x, y) for both equations:

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

   • (0, -5)
   • (1, -3)
   • (2, -1)
   • (3, 1)

2. For \( y = x - 3 \):

   • (0, -3)
   • (1, -2)
   • (2, -1)
   • (3, 0)

Now we will look for a common \( y \)-value for the same \( x \)-value in both equations:

• For \( x = 0 \), \( y = -5 \) from the first equation and \( y = -3 \) from the second equation: no match.
• For \( x = 1 \), \( y = -3 \) from the first equation and \( y = -2 \) from the second equation: no match.
• For \( x = 2 \), \( y = -1 \) from both equations: match.
• For \( x = 3 \), \( y = 1 \) from the first equation and \( y = 0 \) from the second equation: no match.

The only point that satisfies both equations is \( (2, -1) \).

Thus, the solution for the system is:

(2, -1).