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Master the Elimination Method for Solving Linear Systems

Demonstrate an understanding of factors of whole numbers

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Prime factorization

Number properties: Prime or Composite

Number properties: Prime?

Prime factors – Word Problem

Greatest common factors (GCF)

Greatest Common Factor 2 Numbers

Greatest Common Factor 2 Numbers – Word Problem

Least common multiple (LCM)

Lowest Common Multiple - 2 Numbers – Word Problem

Lowest Common Multiple 2 Numbers

Square and square roots

Square Root of a Perfect Square

Cubic and cube roots

Cube root of a perfect cube

Demonstrate an understanding of irrational numbers

Evaluating and simplifying radicals

Rational vs. Irrational numbers

Converting radicals to mixed radicals

Converting radicals to entire radicals

Demonstrate an understanding of powers with integral and rational exponents

Product rule of exponents

Quotient rule of exponents

Power of a product rule

Power of a quotient rule

Power of a power rule

Simplify the power

Negative exponent rule

Combining the exponent rules

Scientific notation

Convert between radicals and rational exponents

Demonstrate an understanding of multiplication of polynomial expressions

Multiplying monomial by monomial

Multiply a Monomial by a Monomial

Multiplying monomial by binomial

Multiplying binomial by binomial

Multiplying polynomial by polynomial

Applications of polynomials

Demonstrate an understanding of common factors and trinomial factoring

Factoring polynomials: ax^2 + bx + c

Factoring Polynomials: ax^2 + bx + c

Factoring perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2

Factoring perfect square trinomials

Find the difference of squares: (a - b)(a + b) = (a^2 - b^2)

Find the difference of squares

Word problems of polynomials

Common factors of polynomials

Factoring polynomials by grouping

Factoring polynomials: x^2 + bx + c

Interpret and explain the relationships among data, graphs and situations

Relationship between two variables

Understand relations between x- and y-intercepts

Domain and range of a function

Identifying functions

Solve problems involving systems of linear equations in two variables

Factor by taking out the greatest common factor

Factor by taking out GCF

Factor by grouping

Factoring difference of squares: \(x^2 - y^2\)

Factoring difference of squares: <katex>x^2 - y^2</katex>

Factoring difference of squares: x^2 - y^2

Factoring trinomials

Factoring Trinomials

Demonstrate an understanding of relations and functions

Graphing from slope-intercept form y=mx+b

Graphing linear functions using a single point and slope

Word problems of graphing linear functions

Function notation

Demonstrate an understanding of slope

Slope equation: \(m = \frac{y_2-y_1}{x_2- x_1}\)

Slope equation: <katex>m = \frac{y_2-y_1}{x_2- x_1}</katex>

Parallel line equation

Perpendicular line equation

Combination of both parallel and perpendicular line equations

Rate of change

Describe and represent linear relations

Slope intercept form:  y = mx + b

Slope intercept form: y = mx + b

General form:  Ax  + By  + C = 0

General form: Ax + By + C = 0

Point-slope form: y - y_1 = m(x - x_1)

Graphing linear functions using table of values

Graphing linear functions using x- and y-intercepts

Determine the characteristics of the graphs of linear relations

Introduction to linear equations

Introduction to nonlinear equations

Special case of linear equations: Horizontal lines

Special case of linear equations: Vertical lines

Parallel and perpendicular lines in linear functions

Relate linear relations expressed in various forms

Determining number of solutions to linear equations

Solving systems of linear equations by graphing

Applications of linear relations

Applications of linear equations

Solving systems of linear equations by elimination

Determine the equation of a linear relation

Money related questions in linear equations

Unknown number related questions in linear equations

Distance and time related questions in linear equations

Rectangular shape related questions in linear equations

Solving systems of linear equations by substitution

Solve problems involving distance between two points and midpoint of a line segment

Distance formula: \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Distance formula: <katex>d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}</katex>

Distance formula

Midpoint formula: \(M = ( \frac{x_1+x_2}2  ,\frac{y_1+y_2}2)\)

Midpoint formula

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2  ,\frac{y_1+y_2}2)</katex>

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)</katex>

Use sine ratio to calculate angles and sides (Sin = o / h)

Use cosine ratio to calculate angles and sides (Cos = a / h)

Use tangent ratio to calculate angles and sides (Tan = o / a)

Represent a linear function using function notation

Combination of SohCahToa questions

Word problems relating ladder in trigonometry

Word problems relating guy wire in trigonometry

Solving expressions using 45-45-90 special right triangles

Solving expressions using 30-60-90 special right triangles

Number Relations and Functions 10

Algebra and Number

Relations and Functions

math

Intro

Ex. 1

<p>- Hi. Welcome to this question right here. So we're trying to solve this system by using a method that's called elimination. Now elimination just kinda means you can actually add 'em or subtract 'em as long as you get rid of one of the variables. And that's all you have to do, okay? So what happened is, if I look into this equation right here, first thing you check is the x line up the x, y lines up the y, the constant lines up the y. . . I mean the constants. Then you double check to see which variable would you like to eliminate. Well, It seems like I've got 4ys on the top and 4ys on the bottom already they are the same. They must be the same for one of the variables. Then in this case I'm going to eliminate y first, because it's already the same from the question, right? So, am I gonna do add, or am I gonna do a subtraction? It's 4y and the minus 4y down here. So think about it. If I just kinda add these two equations right here the 4y plus negative 4y becomes zero. So that way you just eliminate one of your variables, okay? So I am gonna add two equations together. So pretend I'm adding the first equation and the second equation. So 3x plus x, it gives you 4x. This part is zero already. This is equal to. I can put the plug zero right there. Eleven minus seven, we get ourself to four. So to solve for x, it's just gonna turn to solving to one, all right? So if x equals to one, let's see what would y be. Well, you have two choices. All you have to do is you just have to put the x equals to one right in the position of the x. And you can either pick this one, or you can either pick this one. It's up to you. Let's say I do the first one, right? So it's three times the one plus the 4y gives you 11, okay? So I've got three plus the 4y equals to the 11. Then the 4y equals to, put a three over here, you get an eight. Then y equals to two. So, your final answer, if they require you to actually write down the coordinate, it will just be one and two. That's it. Thanks for watching.</p>

Solving a system of linear equations by elimination means by adding or subtracting the equations to get rid of a common variable.  