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 no solution. There is no solution. (3,0) left parenthesis 3 comma 0 right parenthesis There is an infinite number of solutions.

Answer 1

To find the solution for the system of equations represented in Jian's table, we can first analyze the given x-values and their corresponding y-values based on the equations \( y = 2x - 5 \) and \( y = x - 3 \).

Now, we can check each provided (x, y) pair from the table against the two equations to see if they satisfy both equations.

1. For \( (0, -5) \):

   • \( y = 2(0) - 5 = -5 \) (satisfies \( y = 2x - 5 \))
   • \( y = 0 - 3 = -3 \) (does not satisfy \( y = x - 3 \))

2. For \( (1, -3) \):

   • \( y = 2(1) - 5 = -3 \) (satisfies \( y = 2x - 5 \))
   • \( y = 1 - 3 = -2 \) (does not satisfy \( y = x - 3 \))

3. For \( (2, -1) \):

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

4. For \( (3, 1) \):

   • \( y = 2(3) - 5 = 1 \) (satisfies \( y = 2x - 5 \))
   • \( y = 3 - 3 = 0 \) (does not satisfy \( y = x - 3 \))

From the analysis above, the point \( (2, -1) \) meets both equations in the system.

Therefore, the solution for the system is:

(2, -1).