Solution Sets of Simultaneous Equations Quick Check

Question

3 of 53 of 5 Items

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

There is no solution.
There is no solution.
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page 16 of 16

Answer 1

To find the solution for the system of equations \(y = 2x - 5\) and \(y = x - 3\) using the table provided, we need to find the point \((x, y)\) where the outputs for both equations are equal (i.e., when both equations yield the same \(y\) value for a given \(x\)).

From 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 \(x = 2\):

  • \(y = 2(2) - 5 = -1\)
  • \(y = 2 - 3 = -1\) (this is a match)

• For \(x = 3\):

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

Since the only point where both equations yield the same \(y\) value occurs when \(x = 2\) (with both equations giving \(y = -1\)), the solution for this system of equations is:

\((2, -1)\)

Therefore, the correct response is:

(2,−1).