Problem 29 - Beginning and Intermediate Algebra

Question

If an equation in a system contains fractions, what should you do first to make the system easier to solve?

Step-by-Step Solution

Answer

To make a system of equations containing fractions easier to solve, first identify the fractions and find the least common denominator (LCD) among them. Then, multiply each equation by the LCD to eliminate the fractions, and rewrite the system without fractions. Finally, solve the system using a suitable method like substitution or elimination.

Step 1: Identify the fractions in the system of equations

Carefully examine the given system of equations and identify any fractions present. Take note of the denominators for each fraction.

Step 2: Determine the least common denominator (LCD)

Find the least common denominator among all the fractions present in the system. The LCD is the smallest multiple that each of the denominators divides into evenly.

Step 3: Multiply each equation by the least common denominator

For each equation in the system, multiply both sides of the equation by the least common denominator. This will eliminate the fractions, as the denominators will cancel out, leaving behind whole numbers and/or variables.

Step 4: Rewrite the system without fractions

Rewrite the original system of equations, replacing the original equations with the new equations obtained after multiplying by the least common denominator. These new equations should no longer contain fractions.

Step 5: Solve the system without fractions

Use an appropriate method (e.g., substitution, elimination, or matrices) to solve the rewritten system of equations without fractions. This should be much easier and straightforward compared to the original system containing fractions.