Question

solve the linear system using elimination. your answer is an ordered pair (x, y).
8x + y = -16
3x - y = 5

Explanation:

Step1: Write the system of equations

We have the system:

$$\begin{cases} 8x + y = -16 \quad (1)\\ 3x - y = 5 \quad (2) \end{cases}$$

Step2: Eliminate \(y\) by adding equations (1) and (2)

Adding the left - hand sides and the right - hand sides of the two equations:
\((8x + y)+(3x - y)=-16 + 5\)
Simplify the left - hand side: \(8x+y + 3x-y=11x\)
Simplify the right - hand side: \(-16 + 5=-11\)
So we get the equation \(11x=-11\)

Step3: Solve for \(x\)

Divide both sides of the equation \(11x=-11\) by 11:
\(x=\frac{-11}{11}=-1\)

Step4: Substitute \(x = - 1\) into equation (2) to solve for \(y\)

Substitute \(x=-1\) into \(3x - y = 5\):
\(3\times(-1)-y = 5\)
Simplify the left - hand side: \(-3-y = 5\)
Add 3 to both sides: \(-y=5 + 3=8\)
Multiply both sides by - 1: \(y=-8\)

Answer:

\((-1,-8)\)