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Systems of Equations
Example 8

Example 8: Solving Systems

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

Problem

Find x in {3x4y=274x+3y=11\text{Find }x\text{ in }\begin{cases}-3x-4y=-27\\-4x+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

{2x+2y=22x4y=50(x,y)=(9,8)\begin{cases}-2x+2y=-2\\-2x-4y=-50\end{cases}\Rightarrow (x,y)=(9,8)

3. Conclude

(x,y)=(5,3)(x,y)=(5,3)

Final answer

(x,y)=(5,3)(x,y)=(5,3)