Question

Solve the system by substitution.
- 8x + y = -32
- 3x – 10 = y
(,)

Answer 1

Answer:

$x=2,\:y=-16$

Step-by-step explanation:

$\begin{bmatrix}-8x+y=-32\\ -3x-10=y\end{bmatrix}\\\\\mathrm{Isolate}\:x\:\mathrm{for}\:-8x+y=-32:\quad x=-\frac{-32-y}{8}\\\\\mathrm{Subsititute\:}x=-\frac{-32-y}{8}\\\begin{bmatrix}-3\left(-\frac{-32-y}{8}\right)-10=y\end{bmatrix}\\\\Simplify\\\begin{bmatrix}\frac{3\left(-32-y\right)}{8}-10=y\end{bmatrix}\\\\\mathrm{Isolate}\:y\:\mathrm{for}\:\frac{3\left(-32-y\right)}{8}-10=y:\quad y=-16\\\\\mathrm{For\:}x=-\frac{-32-y}{8}\\\\\mathrm{Subsititute\:}y=-16\\x=-\frac{-32-\left(-16\right)}{8}$

$-\frac{-32-\left(-16\right)}{8}=2\\x=2\\x=2,\:y=-16$

Answer 2

Answer:

x = 2

y = -16

Step-by-step explanation:

Substitute value of y, -3x - 10 in the equation-8x + y = -32

-8x + (-3x - 10) = -32

-8x - 3x - 10 = -32

-11x - 10 = -32

-11x = -32 + 10

-11x = -22

Divide both sides by coefficient of x which is -11

x = 2

Substitute value of x, 2, in the equation-3x - 10 = y

(-3)2 - 10 = y

-6 - 10 = y

y = -16