Chapter 9.7, Problem 15IP

To determine

To solve : the given system of equations.

Answer to Problem 15IP

The given system of equations has no solution.

Explanation of Solution

Given information :

The given system of equations:

  $\begin{array}{l}6x+9y=12\\ 2x+3y=6\end{array}$

Calculation :

As per problem,

Consider the system of equations:

  $\begin{array}{l}6x+9y=12\\ 2x+3y=6\end{array}$

Solve the second equation for $x$ .

  $\begin{array}{l}2x+3y=6\text{ [Write the second equation]}\\ 2x+3y-3y=6-3y\text{ [Subtract 3}y\text{ from each side]}\\ 2x=6-3y\text{ [Simplify]}\\ x=3-\frac{3}{2}y\text{ [Divide both sides by 2]}\end{array}$

Substitute $3-\frac{3}{2}y$ for $x$ in the first equation.

  $\begin{array}{l}\text{ 6}x+9y=12\text{ [Write the first equation]}\\ 6\left(3-\frac{3}{2}y\right)+9y=12\text{ [Substitute }x=3-\frac{3}{2}y\text{]}\\ \text{ 18}=12\text{ [Simplify}]\end{array}$

  $18=12$ is a false statement. The system of equations has no solution.