Question

Find the solution set for the equation, given the replacement set.

5x + 2y = –3; {(–2, 9.5), (–3, 11.5), (–4, 8.5), (–5, 6.5)}
a.
{(–2, 9.5), (–3, 11.5)}
c.
{(–4, 8.5)}
b.
{(–3, 11.5)}
d.
{(–4, 8.5), (–5, 6.5)}

Answer 1

c. {(–4, 8.5)}

Explanation:

A plot of the equation and the offered points is attached.

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It might be helpful to put the equation into slope-intercept form.

2y = -5x -3

y = -5/2x -3/2

This shows you that y will be an odd multiple of 1/2 only for even values of x. So, we only need to check the points (-2, 9.5) and (-4, 8.5).

At x=-2, y = -5/2(-2) -3/2 = 5 -3/2 < 9.5 . . . . . (-2, 9.5) is not a solution

At x=-4, y = -5/2(-4) -3/2 = 10 -3/2 = 8.5 . . . . (-4, 8.5) is a solution

Of the offered choices, the only one in the solution set is (-4, 8.5).