Chapter 6.4, Problem 12MCQ

To determine

To solve: the system of linear equation,

Answer to Problem 12MCQ

The value of x and y are 15 and $-\frac{1}{2}$ respectively.

Explanation of Solution

Given information:

The system of equation is,

  $\begin{array}{l}3x+6y=42\mathrm{......}\left(1\right)\\ -7x+8y=-109\mathrm{......}\left(2\right)\end{array}$

Calculation:

Solve the equations by elimination method.

Multiply the equation (2) by -3and equation (1) by 7then subtract from equation (1) as follows:

  $\begin{array}{l}\underset{\_}{\begin{array}{l}21x+42y=294\\ -\left(21x-24y=327\right)\end{array}}\\ 0+66y=-33\\ y=-\frac{1}{2}\end{array}$

Substitute value of y in equation (1) as follows:

  $\begin{array}{c}3x+6\left(-\frac{1}{2}\right)=42\\ 3x-3=42\\ x=15\end{array}$

Thus, the value of x and y are 15 and $-\frac{1}{2}$ respectively.