Question

Courtney and Aaron are having a disagreement. Courtney says that the best way to solve the system ofequations below is by substitution. Aaron argues that the best way to solve the system of equations is byelimination. Who is correct? What is the solution to the system of equations and what is the best way tosolve it?8x + y = -16-3x + y = -5

Answer 1

x=-1

y=-8

Explanation

a) by substitution

Step 1

i) isolate y from equation(1)

$\begin{gathered} 8x+y=-16 \\ y=-16-8x\text{ Equation(3)} \end{gathered}$

ii) now, replace the value of y from equation (3) in equation(2) to find x

$\begin{gathered} -3x+y=-5 \\ -3x-16-8x=-5 \\ -11x=-5+16 \\ -11x=11 \\ x=\frac{11}{-11} \\ x=-1 \end{gathered}$

iii)now, replace the valur of x= -1 in equation (1) to find y

$\begin{gathered} 8x+y=-16 \\ 8\cdot-1+y=-16 \\ -8+y=-16 \\ y=-16+8 \\ y=-8 \end{gathered}$

x=-1, y=-8

Step 2

b)by elimination

i)multiply equation(1) by -1

$\begin{gathered} 8x+y=16\ldots\ldots(-1) \\ -8x-y=16\text{ Equation(3)} \end{gathered}$

ii) add equation(3) and equation(2)

$\begin{gathered} -8x-y=16 \\ -3x+y=-5 \\ _{-------------} \\ -11x=11 \\ x=\frac{11}{-11} \\ x=-1 \end{gathered}$

iii) replace the value of x=-1 in equation (1) to find y

$\begin{gathered} 8x+y=-16 \\ 8\cdot-1+y=-16 \\ -8+y=-16 \\ y=-16+8 \\ y=-8 \end{gathered}$

both methods took the same number of steps, so Aaron and Courtney were right.