Question

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

Answer 1

x = 2

y = -16

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

Answer 2

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

Explanation:

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

`-(-32-\left(-16\right))/(8)=2\\x=2\\x=2,\:y=-16`