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Systems of Equations
Example 9

Example 9: Solving Systems

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

Problem

Find x in {4x−2y=24−x+y=−8\text{Find }x\text{ in }\begin{cases}4x-2y=24\\-x+y=-8\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

{x−4y=−133x−3y=−3⇒(x,y)=(3,4)\begin{cases}x-4y=-13\\3x-3y=-3\end{cases}\Rightarrow (x,y)=(3,4)

3. Conclude

(x,y)=(4,−4)(x,y)=(4,-4)

Final answer

(x,y)=(4,−4)(x,y)=(4,-4)
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