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

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

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

There is no solution.
There is no solution.

(3,0)

Answer 1

To find the solution for the system of equations represented in the table, we need to look for a pair of x- and y-values that satisfy both equations: \( y = 2x - 5 \) and \( y = x - 3 \).

Using the values from the table:

1. For \( x = 0 \):

   • \( y = 2(0) - 5 = -5 \)
   • \( y = 0 - 3 = -3 \)

2. For \( x = 1 \):

   • \( y = 2(1) - 5 = -3 \)
   • \( y = 1 - 3 = -2 \)

3. For \( x = 2 \):

   • \( y = 2(2) - 5 = -1 \)
   • \( y = 2 - 3 = -1 \)
   • Both equations yield \( y = -1 \).

4. For \( x = 3 \):

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

The only pair (x, y) where both equations yield the same y-value is when \( x = 2 \) and \( y = -1 \).

Therefore, the solution for the system is:

(2, -1).