Question

Use the substitution method to solve the linear system. $$\begin{aligned} &3 w-2 u=12\\\ &w-u=60 \end{aligned}$$

Short answer

The solutions to the system of equations are \(u = -168\) and \(w = -108\).

Step-by-step solution

Express One Variable in Terms of the Other

From the second equation \(w-u=60\), isolate \(w\) to get \(w=u+60\).

Substitute for w in the First Equation

We can now substitute \(u+60\) for \(w\) in the first equation to give us \(3(u+60) - 2u = 12\). Simplify this equation by distributing and combining like-terms to get \(3u + 180 - 2u = 12\). This simplifies to \(u + 180 = 12\).

Solve for u

Subtract \(180\) from both sides to get \(u = -168\).

Substitute u in Second Equation

Substitute \(u = -168\) into the second equation \(w = u + 60\). Doing so gives us \(w = -168 + 60\).

Solve for w

Calculate the value of \(w\) which gives \(w = -108\).