Chapter 2.2, Problem 24E

To determine

To find: the solutions of the system of equations

Answer to Problem 24E

  $\begin{array}{l}x=45\\ y=60\end{array}$

Explanation of Solution

Given information:

The given system of equations is as follows:

  $3x+4y=375$  ...(1)

  $5x+2y=345$  ... (2)

Calculation:

Multiply equation (2) by 2 and rewrite the equation as shown below.

  $\begin{array}{l}\left(5x+2y=345\right)2\\ 10x+4y=690\end{array}$  ...(3)

Now, use elimination method to solve equation (1) and (3) as shown below.

  $\begin{array}{l}3x+4y=375\\ 10x+4y=690\\ ---\\ \overline{-7x+0=-315}\\ -7x=-315\\ x=\frac{-315}{-7}\\ =45\end{array}$

Thus, the value of $x$ is 45.

Substitute the value of $x$ in equation (1) and evaluate $y$ as follows:

  $\begin{array}{c}3\left(45\right)+4y=375\\ 135+4y=375\\ 4y=375-135\\ 4y=240\\ y=\frac{240}{4}\\ =60\end{array}$

Thus, the value of $y$ is 60.