Question

1. \\(8x + y = -16\\)\\(-3x + y = -5\\)

Explanation:

Step1: Subtract the two equations

We have the system of equations:

$$\begin{cases} 8x + y = -16 \\ -3x + y = -5 \end{cases}$$

Subtract the second equation from the first equation to eliminate \(y\):
$$(8x + y) - (-3x + y) = -16 - (-5)$$
Simplify the left side: \(8x + y + 3x - y = 11x\)
Simplify the right side: \(-16 + 5 = -11\)
So we get \(11x = -11\)

Step2: Solve for \(x\)

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

Step3: Substitute \(x = -1\) into one of the original equations to solve for \(y\)

Let's use the second equation \(-3x + y = -5\). Substitute \(x = -1\):
$$-3(-1) + y = -5$$
Simplify: \(3 + y = -5\)
Subtract 3 from both sides: \(y = -5 - 3 = -8\)

Answer:

The solution to the system of equations is \(x = -1\) and \(y = -8\)