Question

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

Answer 1

It has two solutions

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 = (8)/(9)`

then for y:

`y = 5(x - 4) \\ y = 5( (8)/(9) - 4) \\ \\ y = 5( - (28)/(9) ) \\ \\ y = - (140)/(9)`