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Systems of Equations
Example 1

Example 1: Solving Systems

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

Problem

Find x in {x−y=13x+3y=−11\text{Find }x\text{ in }\begin{cases}x-y=13\\x+3y=-11\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=−17x−3y=−6⇒(x,y)=(−3,1)\begin{cases}4x-5y=-17\\x-3y=-6\end{cases}\Rightarrow (x,y)=(-3,1)

3. Conclude

(x,y)=(7,−6)(x,y)=(7,-6)

Final answer

(x,y)=(7,−6)(x,y)=(7,-6)
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