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Master Solving Systems of Linear Equations by Graphing

Grade 10 Math: Master Essential Skills & Concepts

1.1 Solving Problems Involving Similar Triangles

Similar triangles

Similar polygons

Proportions

Proportions — Missing Denominator

Proportions — Missing Numerator

Proportions - Find the Missing Denominator LHS

Proportions - Find the Missing Denominator RHS

Proportions - Find the Missing Numerator LHS

Proportions - Find the Missing Numerator RHS

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Combining the exponent rules

Isosceles and equilateral triangles

2.1 Solving Problems Involving the Trigonometry of Right Triangles

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

Solving expressions using 45-45-90 special right triangles

Solving expressions using 30-60-90 special right triangles

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

Pythagorean theorem

Pythagorean Theorem

Using the pythagorean relationship

Applications of pythagorean theorem

3.1 Solving Problems Involving Surface Area and Volume, Using the Imperial and Metric Systems of Measurement

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

1.1 Manipulating and Solving Algebraic Equations

Slope intercept form:  y = mx + b

Slope intercept form: y = mx + b

General form:  Ax  + By  + C = 0

General form: Ax + By + C = 0

Introduction to linear equations

Special case of linear equations: Horizontal lines

Special case of linear equations: Vertical lines

2.1 Graphing and Writing Equations of Lines

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>

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

Rate of change

Parallel and perpendicular lines in linear functions

Applications of linear relations

3.1 Solving and Interpreting Systems of Linear Equations

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

Determining number of solutions to linear equations

Solving systems of linear equations by graphing

Applications of linear equations

Solving systems of linear equations by elimination

Solving systems of linear equations by substitution

1.1 Manipulating Quadratic Expressions

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

Multiplying monomial by monomial

Multiply a Monomial by a Monomial

Multiplying monomial by binomial

Multiplying binomial by binomial

Multiplying polynomial by polynomial

2.1 Identifying Characteristics of Quadratic Relations

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

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

3.1 Solving Problems by Interpreting Graphs of Quadratic Relations

Applications of quadratic functions

Applications of quadratic equations

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Just like your class or textbook, our complete help for grade 10 math includes topics such as Trigonometry, Quadratic Equations, Radicals, Factoring polynomials, Linear equations, Linear systems, and more. Learn the concepts with our video tutorials that show you step-by-step solutions to even the hardest grade 10 math problems. Then, strengthen your understanding with tons of grade 10 math practice. 

All our lessons are taught by experienced grade 10 math teachers. Let&apos;s finish your homework in no time, and ACE that final.

Foundations of Mathematics, Grade 10, Applied (MFM2P) 

1. Measurement and Trigonometry

2. Modelling Linear Relations

3. Quadratic Relations of the Form y = ax^2 + bx + c

math

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Intro

Ex. 1

Intro to solving systems of linear equations by graphing

Three methods for graphing systems of linear equations

- Hello, welcome to this question right here. We're trying to graph these two equations here, and figure out a way they intersect each other, or not, right? 
So, let's go ahead and actually solve in terms of y equals mx plus b, because that's the easiest way to graph this. So, I'm gonna move the y over here and move the negative nine on this side to solve the y. So, I've got myself a 2x plus nine. And this one over here is just going to be, let me do a little bit work here, I'm gonna move the negative x over and I get this, divide everything by three, okay? 
So, now my second equation says negative one over three x plus two, okay? Now, if you have a grid paper, or just a piece of paper is fine, because we're just gonna do a rough sketch to figure out where they intersect each other. So, I've got a positive nine on top, one, two, three, four, five, six, seven, eight, nine. There's a point right there for the first equation, and it's going in this direction, up to over one. That's the slope right there. So, in another way, you can actually do the other direction. So, instead of going up two over one because I ran out of space, I can go down two left one, which is here. And down two left one, which is here. So, I've got myself a nice single straight graph coming down this way, okay? 
Now, if you do the second equation quickly it's actually, your y intercepts at the point y equals two, and the slope is this direction, because it's negative. So, you go down one and over three. So, you go down one and over three, so one, two, three, you're somewhere over here. Two points usually gives you a good point so we're gonna draw a line over here, draw a line over here. Sorry it's not right going straight.okay? 
We've got a little approximate point right here, which is right over here, okay? 
That's a point of intersection. Now, if you're wondering what that point is, it happens at negative three, and a positive three, okay? So, if you have a grid paper, grid paper you can actually plot them really good. And you will see that the both lines right here intersect each other at negative three, and three. Thanks for watching.

Solving a system of linear equations using slope-intercept graphing

Identifying parallel lines with no solution using the intercept method

Graphing two linear equations to find their intersection point

Discovering two equations that simplify to the same line

In order to determine the number of solutions to a system of linear equations, other than by finding the slope of the lines, we can also graph the equations out and look for the intersection of the lines.