Example 5: Solving Systems

Systems of Equations

Example 5

Step-by-step worked example for this lesson track.

Problem

\text{Find }x\text{ in }\begin{cases}2x+y=0\\-4x+4y=12\end{cases}

1. Recognize Pattern

\begin{cases}a_1x+b_1y=c_1\\a_2x+b_2y=c_2\end{cases}

2. Apply Method

\begin{cases}3x-3y=6\\-2x+4y=-18\end{cases}\Rightarrow (x,y)=(-5,-7)

3. Conclude

(x,y)=(-1,2)

Final answer

(x,y)=(-1,2)