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Systems of Equations
Example 2

Example 2: Solving Systems

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

Problem

Find x in {x−3y=−31−2x+2y=30\text{Find }x\text{ in }\begin{cases}x-3y=-31\\-2x+2y=30\end{cases}

1. Recognize Pattern

{a1x+b1y=c1a2x+b2y=c2\begin{cases}a_1x+b_1y=c_1\\a_2x+b_2y=c_2\end{cases}

2. Apply Method

{−4x−5y=194x−y=−1⇒(x,y)=(−1,−3)\begin{cases}-4x-5y=19\\4x-y=-1\end{cases}\Rightarrow (x,y)=(-1,-3)

3. Conclude

(x,y)=(−7,8)(x,y)=(-7,8)

Final answer

(x,y)=(−7,8)(x,y)=(-7,8)
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