Question

How do you substitute to determine if the ordered pair $(3,2)$ is a solution of the system of equations $y=-x+5$ and $x-2y=-4$ ?

Answer 1

Determine the ordered pair in the system of equation

Given: The ordered pair $(3,2)$ and the system of equations $y=-x+5$ and $x-2y=-4$

Therefore

$$\begin{gathered} (x,y)=(3,2) \\ \Rightarrow x=3 \\ \Rightarrow y=2 \end{gathered}$$

We have the equations,

$y=-x+5...\left(1\right)$

$x-2y=-4...\left(2\right)$

If we substitute $x=3$ and $y=2$ in equations $\left(1\right)$ and $\left(2\right)$

Equation $\left(1\right),y=-x+5.$

$$\begin{gathered} \Rightarrow LHS=2 \\ \Rightarrow RHS=-3+5=2 \\ \therefore LHS=RHS \end{gathered}$$

Equation $\left(2\right),x-2y=-4.$

$$\begin{gathered} \Rightarrow LHS=3-2\left(2\right)=-1 \\ \Rightarrow RHS=-4 \\ \therefore LHS\ne RHS \end{gathered}$$

Hence, $(3,2)$ is a solution of $y=-x+5$, but not a solution of $x-2y=-4$.