No.125 A = B = C Systems
POINT
For \(A=B=C\), make a system using any two equalities: \(\begin{cases}A=B\\A=C\end{cases}\qquad\begin{cases}A=B\\B=C\end{cases}\qquad\begin{cases}A=C\\B=C\end{cases}\). Choose the pair that is easiest to calculate.
Solve the following system of equations.
Example
\(2x+y=3x-y=x+5\)
\((x,y)=\left(\frac{10}{3},\frac53\right)\)
Try it yourself.
Solve the following system of equations.
PRACTICE 01
\(x+y=2x-y=6-x\)
PRACTICE 02
\(3x-y=x+3y=2x+2\)
PRACTICE 03
\(2x+3y=4x-y=x+6\)
1. \(x=\frac{12}{5},\ y=\frac65\)
2. \(x=4,\ y=2\)
3. \(x=\frac{12}{5},\ y=\frac65\)