Comparing Methods for Solving Linear Systems

Example 1

Solve the system \(\begin{align*}\begin{cases} 5s+2t=6\\ 9s+2t=22\end{cases}\end{align*}\)

Since these equations are both written in standard form, and both have the term \(\begin{align*}2t\end{align*}\) in them, we will use elimination by subtracting. This will cause the \(\begin{align*}t\end{align*}\) terms to cancel out and we will be left with one variable, \(\begin{align*}s\end{align*}\), which we can then isolate.

\(\begin{align*}& \qquad \ 5s+2t=6\\ &\underline{\;\; - \ (9s+2t = 22) \;\;}\\ & \qquad \ -4s+0t =-16\\ & \qquad \ -4s=-16\\ & \qquad \ s=4\end{align*}\)

\(\begin{align*}5(4)+2t&=6\\ 20+2t&=6\\ 2t&=-14\\ t&=-7\end{align*}\)

The solution is \(\begin{align*}(4,-7)\end{align*}\).