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:

$$
LATEXBLOCK0
$$

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 \(-x + 2y=-15\):

$$
LATEXBLOCK1
$$

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 \((-5,-10)\).