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. (3,0) left parenthesis 3 comma 0 right parenthesis There is no solution.

Answer 1

To find the solution to the system of equations based on Jian's table, we need to analyze the y-values from both equations \(y = 2x - 5\) and \(y = x - 3\).

Let's summarize the y-values given in the table:

• For \(x = 0\):

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

• For \(x = 1\):

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

• For \(x = 2\):

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

• For \(x = 3\):

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

Now let's check the corresponding values for \(x = 2\):

• From \(y = 2x - 5\): When \(x = 2\), \(y = -1\).
• From \(y = x - 3\): When \(x = 2\), \(y = -1\).

Both equations produce the same y-value when \(x = 2\), which is \(-1\). Therefore, the solution to the system is \((2, -1)\).

So, the correct response is:

\((2, -1)\)