Chapter 6.2, Problem 11PPE

To determine

To calculate: solution of the given system of equations using substitution method.

Answer to Problem 11PPE

  $x=2,y=6$

Explanation of Solution

Given information: Equations are $x+y=8,y=3x$

Calculation:

Given equations are $x+y=8,y=3x$

Put $y=3x$ in $x+y=8$

  $\begin{array}{l}x+3x=8\\ \Rightarrow 4x=8\\ \Rightarrow x=\frac{8}{4}=2\end{array}$

Put $x=2$ in $y=3x$

  $y=3(2)=6$

So,

  $x=2,y=6$

Now check whether $x=2,y=6$ is a solution of given system of equations.

Put $x=2,y=6$ in $y=3x$

  $\begin{array}{l}6=3(2)\\ \Rightarrow 6=6\text{which}\text{is}\text{true}\end{array}$

Put $x=2,y=6$ in $x+y=8$

  $\begin{array}{l}2+6=8\\ \Rightarrow 8=8\text{which}\text{is}\text{true}\end{array}$

So, $x=2,y=6$ satisfy the given system of equations.