Question

Use substitution to solve the linear system. $$\begin{aligned} &-6 x-5 y=28\\\ &x-2 y=1 \end{aligned}$$

Short answer

Solution to the system of equations is \(x = -3\) and \(y = -2\).

Step-by-step solution

Isolate Variable in the Second Equation

By rearranging the second equation \(x - 2y = 1\), the variable 'x' can be isolated as follows: \(x = 1 + 2y\)

Substitute 'x' into the First Equation

Substitute \(x = 1 + 2y\) into the first equation \(-6x - 5y = 28\) from the system of equations to get: \[-6(1+2y) - 5y = 28\]. Simplifying this, the equation becomes: \(-12y - 6 - 5y = 28\), and even further simplification gives: \(-17y = 34\)

Solve for 'y'

Solving the equation \(-17y = 34\) for 'y' gives: \(y = -2\)

Substitute 'y' back into the Second Equation

To find 'x' substitute \(y = -2\) back into the second equation from our system. Which gives us \(x - 2(-2) = 1\) which simplifies to \(x = -3\)