Question

Match the system of equations to the number of solutions it has.(4 points)
Put responses in the correct response input area to answer the question. Select a response, navigate to the desired input area and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
x−2y=6 and 3x−6y=18

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y=23x−1 and y=23x−2

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y=5x+7 and 3y−15x=18

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3x+6=y and y=−13x−4

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Answer 1

x − 2y = 6 and 3x − 6y = 18 → Infinitely many solutions (second is 3× first)

y = (2/3)x − 1 and y = (2/3)x − 2 → No solution (parallel, same slope different intercept)

y = 5x + 7 and 3y − 15x = 18 → No solution (second simplifies to y = 5x + 6, different intercept)

3x + 6 = y and y = −13x − 4 → One solution (solve 3x+6 = −13x−4 ⇒ x = −5/8, y = 33/8)