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Systems of Equations
Example 11

Example 11: Solving Systems

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

Problem

Find x in {−4x−4y=−36x−3y=−7\text{Find }x\text{ in }\begin{cases}-4x-4y=-36\\x-3y=-7\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

{3x+5y=−472x+3y=−29⇒(x,y)=(−4,−7)\begin{cases}3x+5y=-47\\2x+3y=-29\end{cases}\Rightarrow (x,y)=(-4,-7)

3. Conclude

(x,y)=(5,4)(x,y)=(5,4)

Final answer

(x,y)=(5,4)(x,y)=(5,4)
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