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Master the Substitution Method for Solving Linear Equations

Grade 10 Math: Master Essential Skills & Concepts

Operations on powers with integral exponents

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Product rule of exponents

Exponents: Product rule (a^x)(a^y) = a^(x+y)

Exponents: Division rule: a^x / a^y = a^(x-y)

Exponents: Power rule: (a^x)^y = a^(xy)

Exponents: Power rule

Exponents: Negative exponents

Exponents: Zero exponent: a^0 = 1

Exponents: Rational 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

Solving for exponents

Prime factorization

Evaluating and simplifying radicals

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

Functions and relations: connecting data, graphs, and situations

Introduction to quadratic functions

Relationship between two variables

Understand relations between x- and y-intercepts

Domain and range of a function

Identifying functions

Function notation

Characteristics of quadratic functions

Transformations of quadratic functions

Quadratic function in general form: y = ax^2 + bx + c

Converting from general to vertex form by completing the square

Shortcut: Vertex formula

Converting general form into vertex form by applying the vertex formula

Vertex Formula Application

Graphing quadratic functions: General form VS. Vertex form

Finding the quadratic functions for given parabolas

Applications of quadratic functions

Quadratic function in vertex form: y = a(x-p)^2 + q

Linear functions: slope and equations of lines

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

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>

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

Graphing from slope-intercept form y=mx+b

Graphing linear functions using a single point and slope

Word problems of graphing linear functions

Parallel line equation

Perpendicular line equation

Combination of both parallel and perpendicular line equations

Rate of change

Parallel and perpendicular lines in linear functions

Applications of linear relations

Arithmetic sequences

Arithmetic series

Arithmetic series formula

Systems of linear equations

Solving 3 variable systems of equations by substitution

Solving 3 variable systems of equations by elimination

Linear programming word problems

Word problems relating 3 variable systems of equations

Solving 3 variable systems of equations (no solution, infinite solutions)

System of Equations With No Solution

System of Equations With Infinite Solutions

System of Equations With Infinite Solutions - Extended

Solving systems of linear equations by graphing

Solving systems of linear equations by elimination

Solving systems of linear equations by substitution

System of linear equations

System of linear-quadratic equations

System of quadratic-quadratic equations

Multiplication of polynomial expressions

What is a polynomial?

Classifying Polynomials

Polynomial components

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

Polynomial factoring

Factoring polynomials: ax^2 + bx + c

Factoring Polynomials: ax^2 + bx + c

Factoring difference of cubes

Factoring sum of cubes

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

Evaluating polynomials

Using algebra tiles to factor polynomials

Solving polynomial equations

Word problems of polynomials

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

Common factors of polynomials

Factoring polynomials by grouping

Solving polynomials with unknown coefficients

Solving polynomials with unknown constant terms

Factoring polynomials: x^2 + bx + c

Applications of polynomials: x^2 + bx + c

Primary trigonometric ratios

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

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

Combination of SohCahToa questions

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

Angle in standard position

Coterminal angles

Coterminal Angles

Reference angle

Find the exact value of trigonometric ratios

ASTC rule in trigonometry (All Students Take Calculus)

ASTC rule in trigonometry

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Foundations of Mathematics and Pre-Calculus 10

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Intro

Ex. 1

- 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? 
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.

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.