Chapter 6, Problem 9SGR

To determine

To describe: Is only addition or subtraction used in elimination method.

Answer to Problem 9SGR

No, in elimination method sometimes division is also used.

Explanation of Solution

Given information:

The elimination method of system of equations.

The steps of performing elimination method are:

Step 1: Write each given equation in standard form $Ax+By=C$ and $A^{\prime }x+B^{\prime }y=C^{\prime }$ .

Step 2: Equate coefficients of one variable equal by multiplying coefficients of variables in both equations. Let for variable “ x ”

  $A^{\prime }Ax+A^{\prime }By=A^{\prime }C$ , and $A{A}^{\prime }x+A{B}^{\prime }y=A{C}^{\prime }$ , then subtracting one equation from other variable “ x ” gets eliminated and remaining equation can be solved for “ y ”.

But some time if expression for one variable is given the division is also applicable.

Let a given system of equations is

  $y=3x+7$  ...... (1)

  $x-y=2$   ...... (2)

From equation (2)

  $y=x-2$  ...... (3)

Dividing equation (1) by equation (3)

  $\frac{y}{y}=\frac{3x+7}{x-2}$

  $\Rightarrow \frac{3x+7}{x-2}=1$

Thus, y gets eliminated and an equation in single variable “ x ” is obtained that can be solved easily.

Conclusion:

In elimination not only addition and subtraction is but sometimes division is also used.