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Systems of Equations
Example 4

Example 4: Solving Systems

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

Problem

Find x in {3x+2y=72x−2y=−22\text{Find }x\text{ in }\begin{cases}3x+2y=7\\2x-2y=-22\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=−7−2x+5y=−41⇒(x,y)=(8,−5)\begin{cases}-4x-5y=-7\\-2x+5y=-41\end{cases}\Rightarrow (x,y)=(8,-5)

3. Conclude

(x,y)=(−3,8)(x,y)=(-3,8)

Final answer

(x,y)=(−3,8)(x,y)=(-3,8)
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