Problem 30 - Beginning and Intermediate Algebra

Question

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

Step-by-Step Solution

Answer

To make a system of equations with decimals easier to solve, first determine the least common multiple (LCM) of the denominators of the decimal numbers. Then, multiply each term of the equation(s) containing decimals by the LCM to eliminate the decimals and convert them into whole numbers. Finally, solve the resulting system of equations using an appropriate method such as substitution, elimination, or matrix methods.

Step 1: Identify the equation with decimals

Look at the system of equations and identify the equation(s) that contain decimal numbers. We will address these decimals to simplify the system.

Step 2: Determine the least common multiple (LCM) of the denominators

To eliminate decimals, determine the least common multiple (LCM) of the denominators of the decimal numbers. To do this, first identify the smallest integer that is divisible by all the denominators.

Step 3: Multiply the equation by the LCM

To eliminate the decimals, multiply each term of the equation(s) containing decimals by the least common multiple (LCM) found in the previous step. This process will convert the decimals into whole numbers, making the system of equations easier to solve.

Step 4: Solve the resulting system of equations

After multiplying the equation(s) by the LCM and converting the decimals into whole numbers, proceed to solve the resulting system of equations using any suitable method such as substitution, elimination, or matrix methods.