Question

Solve the following system of equations using the substitution method.–y = 5x + 21 –4x + y = 6

Answer 1

The solution:

Given:

$\begin{gathered} -y=5x+21...eqn(1) \\ -4x+y=6...eqn(2) \end{gathered}$

Required:

To solve by the Substitution Method.

From eqn(1), we get:

$y=-5x-21...eqn(3)$

Putting eqn(3) into eqn(2), we get:

$-4x+(-5x-21)=6$

Clear the bracket:

$\begin{gathered} -4x-5x-21=6 \\ \\ \text{ Collect the like terms:} \\ -9x=6+21 \\ \\ -9x=27 \end{gathered}$

Divide both sides by -9.

$x=\frac{27}{-9}=-3$

Substitute -3 for x in eqn(3), we get:

$y=-5(-3)-21=15-21=-6$

Thus, the correct answer is (-3,-6)