Question

Determine the number of solutions you will have for the system 4y + x = 16 and y = 4 – x.

Answer 1

Equaling both equations, it is found that the correct option that states the number of solutions you will have for the system is:

• D: one solution

The equations are:

$4y + x = 16 \rightarrow x = 16 - 4y$

$y = 4 - x \rightarrow x = 4 - y$

Equaling both equations for x, we have that:

$16 - 4y = 4 - y$

$3y = 12$

$y = \frac{12}{3}$

$y = 4$

$x = 4 - y = 4 - y = 0$

Hence, the system has one solution, which is (0,4), and option d is correct.

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