Question

question find the solution of the system of equations. \\(-x - 8y = 2\\) \\(x - 5y = -15\\) answer attempt 1 out of 2 (\\(square\\), \\(square\\)) submit answer

Explanation:

Step1: Write the system of equations

We have the system:

$$\begin{cases} -x - 8y = 2 \\ x - 5y = -15 \end{cases}$$

Step2: Add the two equations to eliminate \(x\)

Adding the left - hand sides and the right - hand sides of the two equations:
\((-x - 8y)+(x - 5y)=2+(-15)\)
Simplify the left - hand side: \(-x - 8y+x - 5y=-13y\)
Simplify the right - hand side: \(2-15 = - 13\)
So we get the equation \(-13y=-13\)

Step3: Solve for \(y\)

Divide both sides of the equation \(-13y = - 13\) by \(-13\):
\(y=\frac{-13}{-13}=1\)

Step4: Substitute \(y = 1\) into one of the original equations to solve for \(x\)

Let's substitute \(y = 1\) into the second equation \(x-5y=-15\)
We have \(x-5\times1=-15\)
Simplify: \(x - 5=-15\)
Add 5 to both sides of the equation: \(x=-15 + 5=-10\)

Answer:

\((-10,1)\)