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Master the Substitution Method for Solving Linear Equations

Grade 10 Math: Master Essential Skills & Concepts

FP10.1

auto-gen

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

FP10.10

Determining number of solutions to linear equations

Solving systems of linear equations by graphing

Solving systems of linear equations by elimination

Solving systems of linear equations by substitution

FP10.2

Evaluating and simplifying radicals

Product rule of exponents

Rational vs. Irrational numbers

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

Convert between radicals and rational exponents

Converting radicals to mixed radicals

Converting radicals to entire radicals

FP10.3

Conversions between metric and imperial systems

Metric to Imperial Conversions

Imperial to Metric Conversions

Conversions Between Metric and Imperial Systems Speed KM to MI

Conversions Between Metric and Imperial Systems Speed  MI to M

Metric-Imperial Length Conversion Inch To Cm

Metric-Imperial Length Conversion MM/CM/M/KM To FT

Metric-Imperial Length Conversion MM/CM/M/KM To MI

Metric systems

Add and Subtract Mixed Units

Metric Length Conversion

Add or Subtract Different Metric Units Convert to CM

Add or Subtract Different Metric Units Convert to M

Add or Subtract Different Metric Units Convert to MM

Imperial systems

Imperial Length Conversion

Conversions involving squares and cubic

Imperial to Metric Conversions — Squares and Cubes

Imperial Conversion — Squares and Cubes

Metric to Imperial Conversion — Squares and Cubes

Metric Area Conversion FT to CM

Metric Area Conversion Foot to Inch

Metric Area Conversion M/CM to Inch

Surface area and volume of prisms

Surface area and volume of pyramids

Surface area and volume of cylinders

Surface area and volume of cones

Surface area and volume of spheres

FP10.4

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

Word problems relating ladder in trigonometry

Word problems relating guy wire in trigonometry

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

FP10.5

Solving polynomials with the unknown "b" from ax^2 + bx + c

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

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

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

FP10.6

Relationship between two variables

Understand relations between x- and y-intercepts

Domain and range of a function

Identifying 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

FP10.7

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)

Rate of change

FP10.8

Graphing linear functions using table of values

Graphing linear functions using x- and y-intercepts

Introduction to linear equations

Introduction to nonlinear equations

Special case of linear equations: Horizontal lines

Special case of linear equations: Vertical lines

Parallel line equation

Perpendicular line equation

Combination of both parallel and perpendicular line equations

FP10.9

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

Applications of linear equations

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Foundations of Mathematics and Pre-calculus 10

Number Sense

math

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https://dmn92m25mtw4z.cloudfront.net/img/textbook/textbook-grade10math.png

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.