Chapter 6, Problem 6SGR

To determine

To state: The given statement is true or false. If false replace underlined term to make a true sentence.

Answer to Problem 6SGR

The given statement is true.

Explanation of Solution

Given information:

The given statement:

In some cases dividing two equations in a system together will eliminate one of the variable. This process is called elimination.

Concept used:

In the method of elimination for two linear equations in standard form $Ax+By=C$ and $A^{\prime }x+B^{\prime }y=C^{\prime }$ , first we make coefficients of one variable equal then add two equations if signs of coefficients are equal and subtract of signs of variable are same. In this way, one variable gets eliminated.

But some time we can eliminate one variable by dividing two equations also.

Suppose $x+2y=7$ and $2x-y=4$ are two given equation. Then from equation $x+2y=7$ ,

  $x=7-2y$........ (1)

From equation (2)

  $2x=4-y$........ (2)

Dividing equation (2) by equation (1)

  $\frac{2x}{x}=\frac{4-y}{7-2y}$

  $2=\frac{4-y}{7-2y}$ .

Thus, the variable ‘ x’ gets eliminated.

Hence, the given statement is true.

Conclusion:

The given statement is true.