Solving Rational Equations and Quadratics

The video tutorial explains how to solve systems of rational equations using substitution and cross-multiplication. It provides a detailed walkthrough of solving two different systems, including factoring quadratic equations and finding corresponding y-values. The tutorial concludes with additional resources for further learning.

What is the first step in solving systems of rational equations using substitution?

• Set the expressions equal to each other

• Set the expressions equal to zero

• Multiply both sides by a constant

• Add the expressions together

When cross-multiplying two fractions, what is the result?

• The sum of the numerators

• The product of the denominators

• The product of the cross terms

• The difference of the numerators

What is the quadratic equation derived from the rational equations in the lesson?

• x^2 - 3x + 28 = 0

• x^2 + 3x - 28 = 0

• x^2 - 3x - 28 = 0

• x^2 + 3x + 28 = 0

Which pair of numbers is used to factor the quadratic equation x^2 + 3x - 28?

• -4 and -7

• 4 and 7

• -4 and 7

• 4 and -7

What are the solutions for x in the quadratic equation x^2 + 3x - 28 = 0?

• x = -4 and x = -7

• x = 4 and x = -7

• x = -4 and x = 7

• x = 4 and x = 7

How do you find the corresponding y values for the solutions of x?

• By multiplying the solutions of x

• By substituting x into the original equation

• By dividing the solutions of x

• By adding the solutions of x

What is the first step in solving the new system of rational equations?

• Solve for y

• Solve for x

• Add the equations

• Eliminate the fractions

What operation is used to eliminate fractions in the new system of equations?

• Addition

• Subtraction

• Multiplication

• Division

What are the solutions for x in the new system of equations?

• x = 9 and x = 7

• x = -9 and x = 7

• x = 9 and x = -7

• x = -9 and x = -7

What are the ordered pairs for the solutions of the new system of equations?

• (9, 4) and (-7, -4/3)

• (9, -4/3) and (-7, 4)

• (7, 4) and (-9, -4/3)

• (7, -4/3) and (-9, 4)