Question
Solution Sets of Simultaneous Equations Quick Check
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
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.
Skip to navigation
page 16 of 16
Answers
GPT-4o mini
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)**.
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)**.
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