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).