Skip to content
Systems of Equations
Example 6

Example 6: Solving Systems

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

Problem

Find x in {3x4y=64x+4y=20\text{Find }x\text{ in }\begin{cases}3x-4y=-6\\4x+4y=20\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

{5xy=36x2y=18(x,y)=(6,6)\begin{cases}5x-y=-36\\x-2y=-18\end{cases}\Rightarrow (x,y)=(-6,6)

3. Conclude

(x,y)=(2,3)(x,y)=(2,3)

Final answer

(x,y)=(2,3)(x,y)=(2,3)