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Systems of Equations
Example 12

Example 12: Solving Systems

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

Problem

Find x in {−3x−y=−5−3x−4y=−11\text{Find }x\text{ in }\begin{cases}-3x-y=-5\\-3x-4y=-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

{3x−2y=−105x−y=−5⇒(x,y)=(0,5)\begin{cases}3x-2y=-10\\5x-y=-5\end{cases}\Rightarrow (x,y)=(0,5)

3. Conclude

(x,y)=(1,2)(x,y)=(1,2)

Final answer

(x,y)=(1,2)(x,y)=(1,2)
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