Chapter 3 - Linear And Quadratic Equations

Question 1

What are two common methods to solve a system of equations with different variables?

Answer 1

1) The Substitution Method

2) The Combination Method

Question 2

How do you apply the substitution method to solve a system of equations?

Answer 2

1) Isolate one of the variables in either equation

2) Substitute that variable into the other equation

Question 3

How do you apply the combination method to solve a system of equations?

Answer 3

1) Add one equation to the other, or subtract one equation from the other in order to eliminate one of the variables
2) Solve for the other variable

Note: Be sure to add/subtract the entire equation, not just the variable you’re eliminating

Question 4

How can you apply the combination when the coefficients of each variable are different in the two equations?

Answer 4

Manipulate the equation by multiplying it so that the coefficient matches that of the variable you’re trying to eliminate in the other equation

Question 5

When should you use the substitution method?

Answer 5

When one of the equations can be easily manipulated to isolate one of the variables on one side of the equation

Question 6

When should you use the combination method?

Answer 6

when neither equation can easily be manipulated to solve for one of the variables

Question 7

How can we eliminate fractions in an equation?

Answer 7

Multiply the entire equation by the LCM of the denominators of all the fractions in the equation

Question 8

What does it mean if you’re asked to “solve for x in terms of y”?

Answer 8

To solve for x in terms of y simply means to manipulate the equation such that x is isolated on one side of the equal sign, and the expression containing y on the other.

Question 9

When is the product of two integers = 1?

Answer 9

When both factors are either 1 or -1

Question 10

What is the Zero Product property?

Answer 10

The product of two quantities equals 0 when one or both of the two factors is 0.

Question 11

What is a quadratic equation?

Answer 11

An equation where the highest power of a variable is 2 (squared)

Question 12

What is standard form for a quadratic equation?

Answer 12

ax^2 +bx + c = 0

Question 13

What is (x + y)^2 in standard form?

Answer 13

x^2 + 2xy + y^2

Question 14

What is (x-y)^2 in standard form?

Answer 14

x^2 - 2xy + y^2

Question 15

What is (x+y)(x-y) in standard form?

Answer 15

x^2 - y^2 (aka, the difference of two squares)

Question 16

if x ≠ y, (x-y)/(y-x) = ?

Answer 16

(x-y)/(y-x) = -1