Question

For the following system of equations, determine how many solutions there are. y = 5(x − 4) and 4x + 12 = −y

Answer 1

Answer:

It has two solutions

Step-by-step explanation:

$y = 5(x - 4)$

substitute for y in second equation:

$4x + 12 = - y \\ 4x + 12 = - \{5(x - 4) \} \\ 4x + 12 = - 5x + 20 \\ 9x = 8 \\ x = \frac{8}{9}$

then for y:

$y = 5(x - 4) \\ y = 5( \frac{8}{9} - 4) \\ \\ y = 5( - \frac{28}{9} ) \\ \\ y = - \frac{140}{9}$