Algebra and Equation Solving module (videos 15-26)

¡Supera tus tareas y exámenes ahora con Quizwiz!

1. Find Solution 2. Identical Equations 3. 0x+0y = a number

1. 1 solution 2. infinite solutions 3. nonzero value (zero solutions)

Second method to solving

Elimination Method

Video 24

Equations and Powers

A question that might require an understanding of √(b²-4ac) part of a quadratic equation.

There's a data sufficiency question that might result in a negative inside a square root. Because you can't solve a number with a negative square root, it would be impossible to solve.

3x + 2y = 9 6x + 4y = 11

These equations contradict each other. Therefore, there's no solution

True or False? IxI = x if x ≥ 0

True

Absolute Value

a number's distance from zero on a number line

Isolate the variable (x) by performing the same operations to ____ ______

both sides

√x = 5 How do you pull x out of the square root?

Square both sides

A solution to an equation can also be referred to as the ______

root x=5 would be the root

(a/b)(b/a) = ?

1 Remember, what you do on the l

4 steps for the Elimination Method

1) Manipulate equations until you have matching coefficients for one variable 2) Add or subtract 2 equations to eliminate one variable 3) Solve for the remaining variable 4) Plug the solution into any equation to solve for the other variable

If AB=0. What values could A and B be?

A could be 0, B could be 0, or both could be 0

VIDEO 26!!!!!!!!!!!!!

Absolute Value Question

List the equations that are quadratic. 1. 3x² - 2x - 1 = 8 2. x² - 9 = 0 3. x² + 7x = 0

All of them are quadratic. Remember, as long as (a≠0)

Extraneous Roots

An answer that appears to be legitimate, but it's not.

Linear Equation

Ax+By = C (2 unknown variables)

Video 17

Quadratic Equations

Video 18

Rational Sum of Solutions

Golden Rule of Equation Solving

What you do to one side of the equation, you must do to the other side.

Quadratic equation

an equation of the form ax² + bx + c = 0, where a ≠ 0

If (b² - 4ac) < 0, is there a solution? What if (b² - 4ac) ≥ 0, is there a solution?

1. No solution exists 2. Solution exists

Does this trick work with bases as 0's? o^x = 0^y?

No

Does this trick work with bases as 1's (positive and negative)?

No

³√(3x+11) = 2

Not extraneous, since it's a cube root

Video 21

Number of Solutions to a System

First method to solving linear equations 3x + 7 = 17 2x - 2y = 6

The substitution method (solve for one variable in the first equation, either x or y, and then plug it into the other equation)

(√k)² = __

k (for k ≥ 0)

Video 19

2 Equations with 2 Unknowns

Video 22

3 Equations with 3 Unknowns

Part 2 (statement 2 alone)

B.

Video 15

Basic Equation Solving

Video 16

Eliminating Fractions

If 3x - 4y = 3 and 2x - 5y = 5, then x + y = A) -2 B) -1 C) 0 D) 1 E) 2

Long Solution

Most quadratic equations will have ___ possible solutions

two

If b^x = b^y then _______

x = y

IxI = 4

x must be 4 or -4 Applies to all x's IxI = a or -a

x²+2x-24=0

x= -6 or 4

Are these types of questions rare on the GMAT? (3 equations with 3 unknowns)

yes

A system of 2 equations with 2 variables can have ___ solutions, ___ solution or ________ solutions

1. zero 2. one 3. infinitely many

Video 23

Equations with Square Roots

Steps to solve 3 equations with 3 unknowns

1) Solve one equation for one variable 2) Take the other two equations and replace the chosen variable with its equivalent expression from the first equation 3) Solve for the two remaining variables 4) Plug the solution into any equation to solve for the third variable or 1)Solve using the elimination method

Steps for the Substitution Method

1. Solve one equation for one variable 2. Take the other equation and replace the chosen variable with its equivalent expression from the first equation. 3. Solve for the variable 4. Plug the solution into any equation to solve for the other variable.

Video 25

Equations with Absolute Value

What is the value of x? 1) |x-10| = 6 2) |x²-16| = x - 4|

Part 1 (statement 1 alone)

√(5 - x) = √(2x - 13) Solve for x

Square root of -1 doesn't exist

Video 20

System Question


Conjuntos de estudio relacionados

Cognitive Psychology: The Acquisition of Memories and the Working-Memory System

View Set

Ch 9 Domestic U.S. and Global Logistics

View Set

Endocrine NCLEX Practice Questions

View Set

Intro to public speaking Midterm study guide

View Set

A&P II: Chapter 22 - The Respiratory System

View Set

AP EURO-Chapter 19: A Revolution in Politics: The Era of the French Revolution and Napoleon

View Set

Meteorology: Chapter 13: Weather Forecasting

View Set