Question

State whether each sentence is true or false. If false, replace the underlined term to make a true sentence.

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

Short answer

The given statement is false. The corrected statement is:

“In some cases, adding or subtracting two equations in a system together will eliminate one of the variables. This process is called elimination.”

Step-by-step solution

Step 1. State the concept of substitution method.

The elimination method is the method in which addition/subtraction/scalar multiplication method is used to get an equation in the one variable.

Step 2. Explanation of the statement.

Since, a system of two linear equations can be solved using elimination method in these two ways:

1. If the coefficients are opposite, use the addition and when the coefficients are same, use the subtraction.
2. If the coefficients are neither same in value and opposite in sign nor same in value and same in sign, then they are multiplied by a scalar to make the coefficients equal and then the equations are added or subtracted accordingly.

Step 3. Write the correct statement.

So, the given statement gives that dividing two equations in the elimination method is used to get an equation in the one variable. It is incorrect.

Hence, the given statement is false. The corrected statement is:

“In some cases, adding or subtracting two equations in a system together will eliminate one of the variables. This process is called elimination.”