How To Solve Systems of Rational Equations - Algebra

TL;DR

Learn how to solve systems of rational equations by using substitution and factoring.

Transcript

in today's lesson we're going to talk about how to solve systems of rational equations so here we have two rational functions and our goal is to solve for x and y in this problem now because these two expressions equal y that means that they equal each other so we can solve by substitution we could set these two expressions equal to each other when... Read More

Key Insights

• 😑 Systems of rational equations can be solved by setting the two expressions equal to each other and solving for x.
• 🧑‍🏭 Factoring quadratic trinomials is necessary to find the solutions to rational equations.
• 0️⃣ The zero product property is used to set each factor equal to zero and find the possible solutions.
• ☺️ Substituting the values of x back into one of the original equations helps find the corresponding values of y.

Questions & Answers

Q: What is the goal when solving systems of rational equations?

The goal is to find the values of x and y that satisfy both equations in the system.

Q: How can we solve systems of rational equations by substitution?

We can set the two expressions equal to each other and solve the resulting equation for x. Then, we can substitute the value of x back into one of the original equations to find the corresponding value of y.

Q: What is the zero product property and how is it used in solving rational equations?

The zero product property states that if the product of two factors is zero, then at least one of the factors must be zero. In solving rational equations, we set each factor equal to zero and solve for x.

Q: How do we factor quadratic trinomials in order to solve rational equations?

We look for two numbers that multiply to the constant term and add up to the coefficient of the linear term. By factoring the trinomial, we can find the two possible solutions for x.

Summary & Key Takeaways

• The content discusses how to solve systems of rational equations using substitution and factoring.

• It provides step-by-step instructions on how to solve the equations and find the corresponding values of x and y.

• The video also offers additional resources for further learning about rational expressions and graphing rational functions.