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Systems of Equations
Example 3

Example 3: Solving Systems

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

Problem

Find x in {2x−4y=32x−3y=23\text{Find }x\text{ in }\begin{cases}2x-4y=32\\x-3y=23\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

{−5x−2y=−505x+3y=55⇒(x,y)=(8,5)\begin{cases}-5x-2y=-50\\5x+3y=55\end{cases}\Rightarrow (x,y)=(8,5)

3. Conclude

(x,y)=(2,−7)(x,y)=(2,-7)

Final answer

(x,y)=(2,−7)(x,y)=(2,-7)
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