Question

solve the system of equations $-6x - y = 2$ and $-5x - y = 0$ by combining the equations.

Explanation:

Step1: Combine the two equations

We have the two equations:
\(-6x - y = 2\) (Equation 1)
and after multiplying the second equation \(-5x - y = 0\) by \(-1\), we get \(5x + y = 0\) (Equation 2)

Now, add Equation 1 and Equation 2 together:
\((-6x - y)+(5x + y)=2 + 0\)

Simplify the left - hand side:
\(-6x - y+5x + y=-x\)
The right - hand side is \(2\). So we have the equation \(-x = 2\)

Step2: Solve for \(x\)

To solve for \(x\) in the equation \(-x=2\), we multiply both sides of the equation by \(- 1\).
\(x=-2\)

Step3: Substitute \(x = - 2\) into one of the original equations to solve for \(y\)

Let's substitute \(x=-2\) into the equation \(-5x - y = 0\)
\(-5\times(-2)-y = 0\)
First, calculate \(-5\times(-2)=10\), so the equation becomes \(10 - y = 0\)
Subtract 10 from both sides: \(-y=-10\)
Multiply both sides by \(-1\): \(y = 10\)

Answer:

The solution to the system of equations is \(x=-2\) and \(y = 10\)