Solving Systems of Equations With Fractions and Decimals

TL;DR

Learn how to solve equations involving fractions and decimals by clearing away all the fractions or using substitution method.

Transcript

now sometimes you may have fractions or decimals in these equations what do you think we need to do in order to solve these two equations let's say if we have this particular equation what would you do whenever you have fractions you can make the process a lot easier if you try to clear away all fractions in the first equation let's multiply everyt... Read More

Key Insights

• 💨 Clearing away fractions in an equation involves multiplying every term by the common denominator.
• ✖️ The elimination method is useful when x or y terms can be made equal by multiplying one or both equations.
• ❓ Substitution method is preferred when one variable can be easily isolated in one of the equations.
• ❣️ After obtaining the values for x and y, it is important to check if they satisfy both equations by substituting them back in.

Questions & Answers

Q: How can we simplify equations with fractions?

To simplify equations with fractions, multiply every term by the common denominator to eliminate the fractions. This allows us to work with whole numbers and simplifies the equation.

Q: When should we use the elimination method?

The elimination method is best used when the coefficients in front of x or y in both equations can be easily made equal. By multiplying one or both equations, we can eliminate one variable and solve for the other.

Q: How do we solve equations with decimals using substitution?

To solve equations with decimals using substitution, replace one variable with its equivalent expression from the other equation. This allows us to create an equation with only one variable and solve for its value.

Q: What should be done after finding the values for x and y?

After finding the values for x and y, substitute them back into one of the original equations to ensure that they satisfy both equations. This allows us to verify the solution.

Summary & Key Takeaways

• To solve equations with fractions, multiply every term by the common denominator to clear away the fractions.

• To solve equations with decimals, use substitution method by replacing one variable with its equivalent expression from the other equation.

• After obtaining the values for x and y, substitute them back into one of the original equations to find the solution.