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Master the Substitution Method for Solving Linear Equations

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 back to this question here. So we're going to solve these two equations and try to find the x and y, but you must use these substitutions. Substitutions just mean that you either take this y over here, you plug in this y over here. Or you take this x, plug in this x over here. Or vice versa, okay. It could be upside-down. But y goes in the y, x goes in the x okay. So what I would do is, I would suggest that you want to take a look at your two equations first and you might want to pick the one that seems easier. Like the first one, if you solve for y for the first one wouldn't it be just 6x minus seven equals y, okay?<br />
Because remember you want to solve for one variable it could be the x it could be the y, but in this case I chose the y. So what I'm going to do is take this y over here and I'm going to plug it into the second equation where the y is, y goes into y. Because these two equations are equal somewhere on the graph. So their x and y, which is a coordinate, will be the same. So that's why I'm allowed to actually take this y here and plug it into another equation's y. So let's go ahead and actually solve this equation here. So after I plug it in what that means is this y will represent this whole thing here, which is 6x minus seven. So I'm going to put a 6x minus seven in the bracket, it has to be in the bracket. If you don't you're in trouble. Copy down everything and expand this, so two, six gives you 12. That's my 12 right there, and that's a 14 here and and equals to seven okay. Now look at the calculator by yourself, that's actually 12 minus nine I can do that in my head. 14 comes over here. I think that's just 21, right? So and then you get yourself x equals to just a 7. So you found your x. So after you find one of your variables you plug it in back to your original equation up here. Either the first one or the second one, doesn't matter. Let's say you do the first one, it will be six times seven minus y equals to seven. What's six times seven, six times seven is 42, so you get yourself 42 minus y equals to seven. Yes I'm using a calculator for all of these because I'm nervous when I'm in front of a camera. Thirty-five. I bring the seven over and I bring the y over to the other side. So I get y equals to 35, okay. Now if this is a coordinate on your graph, you will have to write down seven and 35, is the point that these two equations are going to intersect each other, okay. Thanks for watching.</p>


Another way to solve systems of linear equations is by substitution. We can substitute the y/x in one of the equations with the y/x in the other equation.