Question

Solve the system by elimination$\left\{\begin{array}{l}x+2y=6\\ y=-\frac{1}{2}x+3\end{array}\right.$

Short answer

The equations are consistent and dependent

Step-by-step solution

Given information

Given the system of equations$\left\{\begin{array}{l}x+2y=6\\ y=-\frac{1}{2}x+3\end{array}\right.$

Substitution of value of variable in another equation

Substituting in another equation, we get

$$\begin{gathered} y=\frac{-1}{2}x+3 \\ y=\frac{-1}{2}(6-2y)+3 \\ y=\frac{-1}{2}.6-\frac{1}{2}(-2y)+3 \\ y=-3+y+3 \\ -3=-3 \end{gathered}$$

The equations are consistent and dependent