Algebra and Equation Solving module (videos 15-26)
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