Chapter 6, Problem 49SGR

To determine

the best method to solve each system of equation.

Answer to Problem 49SGR

The solution is: $x=2,y=5$ .

Explanation of Solution

Given:

  $\begin{array}{l}3x+4y=26\\ 2x+3y=19\end{array}$

Calculation:

Here, the equations are:

  $3x+4y=26\dots \dots \left(1\right)$

And,

  $2x+3y=19\dots \dots \left(2\right)$

The strategy is to solve the system of equations using the best method.

The best method to solve the system is the elimination method.

Multiply (1) by 3 to get:

  $\begin{array}{l}3\left(3x+4y\right)=3\left(26\right)\\ 9x+12y=78\dots \dots \left(3\right)\end{array}$

Again, multiply (2) by 4:

  $\begin{array}{l}4\left(2x+3y\right)=4\left(19\right)\\ 8x+12y=76\dots \dots \left(4\right)\end{array}$

Subtract equation (4) from (3) to get:

  $\begin{array}{l}\left(9x+12y\right)-\left(8x+12y\right)=78-76\\ 9x+12y-8x-12y=2\\ x=2\end{array}$

From equation (1),

  $\begin{array}{l}3\left(2\right)+4y=26\\ 6+4y-6=26-6\\ \frac{4y}{4}=\frac{20}{4}\left[\text{Divide both sides by 4}\right]\\ y=5\end{array}$

Conclusion:

Hence, the solution is: $x=2,y=5$ .