Question

question find the solution of the system of equations. \\(-x + 2y = -15\\) \\(8x - 2y = -20\\)

Explanation:

Step1: Label the equations

Let the first equation be \(-x + 2y=-15\) (Equation 1) and the second equation be \(8x - 2y=-20\) (Equation 2).

Step2: Eliminate \(y\) by adding the two equations

Add Equation 1 and Equation 2:
\[

$$\begin{align*} (-x + 2y)+(8x - 2y)&=-15+(-20)\\ -x + 2y+8x - 2y&=-35\\ 7x&=-35 \end{align*}$$

\]

Step3: Solve for \(x\)

Divide both sides of \(7x = - 35\) by 7:
\[x=\frac{-35}{7}=-5\]

Step4: Substitute \(x = - 5\) into Equation 1 to find \(y\)

Substitute \(x=-5\) into \(-x + 2y=-15\):
\[

$$\begin{align*} -(-5)+2y&=-15\\ 5 + 2y&=-15 \end{align*}$$

\]
Subtract 5 from both sides:
\[2y=-15 - 5=-20\]
Divide both sides by 2:
\[y=\frac{-20}{2}=-10\]

Answer:

The solution of the system of equations is \(x = - 5\) and \(y=-10\), or the ordered pair \((-5,-10)\).