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Systems of Equations
Example 10

Example 10: Solving Systems

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

Problem

Find x in {−4x−2y=−26−3x−2y=−18\text{Find }x\text{ in }\begin{cases}-4x-2y=-26\\-3x-2y=-18\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−y=29−x−2y=−23⇒(x,y)=(9,7)\begin{cases}4x-y=29\\-x-2y=-23\end{cases}\Rightarrow (x,y)=(9,7)

3. Conclude

(x,y)=(8,−3)(x,y)=(8,-3)

Final answer

(x,y)=(8,−3)(x,y)=(8,-3)
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