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Master the Substitution Method for Solving Linear Equations

8.EE.A.1

Using exponents to describe numbers

Expanded powers

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Exponent rules

Single Power Expressions

Dividing powers

Multiplying powers

Order of operations with 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

8.EE.A.2

Squares and square roots

Square Root of a Perfect Square

Square and square roots

Cubic and cube roots

Cube root of a perfect cube

Converting radicals to mixed radicals

Converting radicals to entire radicals

8.EE.A.3

Scientific notation

8.EE.B.5

Parallel and perpendicular lines in linear functions

Understanding graphs of linear relationships

Linear relations

Understanding tables of values of linear relationships

Linear relation

Applications of linear relationships

Identifying proportional relationships

8.EE.B.6

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

8.EE.C.7

Introduction to linear equations

Model and solve one-step linear equations: ax = b, x/a = b

One-step Linear Equations

One Step Linear Equations — Word Problem

One-step equations

One-step Equations LHS

One-step Equations RHS

Model And Solve One Step Linear Equations Divide – Word Problem

Model And Solve One Step Linear Equations Multiply – Word Problem

Solving two-step linear equations using addition and subtraction: ax + b = c

Two-step Linear Equations

Two-step Linear Equations LHS

Solve Linear Equations Using Addition and Subtraction – Word Problem

Two-step Linear Equations — Word Problem

Solving two-step linear equations using multiplication and division: x/a + b = c

Two-step Linear Equations RHS

Solving two-step linear equations using distributive property: a(x + b) = c

Solve Linear Equations Using Distributive Property – Word Problem

Solving literal equations

8.EE.C.8

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

8.F.A.1

Relationship between two variables

Identifying functions

8.F.A.2

Function notation

8.F.B.4

Applications of linear relations

8.F.B.5

Graphing linear functions using table of values

8.G.A.1

Line symmetry

Tessellations using translations and reflections

tessellations using translations and reflections

8.G.A.2

Rotational symmetry and transformations

8.G.A.3

Enlargements and reductions with scale factors

Tessellations using rotations

8.G.A.4

Similar polygons

8.G.A.5

Similar triangles

8.G.B.6

Pythagorean theorem

Pythagorean Theorem

8.G.B.7

Using the pythagorean relationship

8.G.B.8

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

Applications of pythagorean theorem

8.G.C.9

Volume of cylinders

Word problems relating volume of prisms and cylinders

Surface area and volume of cones

Surface area and volume of spheres

8.NS.A.1

Understanding the number systems

Rational vs. Irrational numbers

8.NS.A.2

Determine square roots of rational numbers

Square roots of rational numbers

Estimating square roots

Converting repeating decimals to fractions

8.SP.A.1

Reading linear relation graphs

Box-and-whisker plots and scatter plots

8.SP.A.2

Solving linear equations by graphing

8th Grade Math

sample

math

Intro

Ex. 1

Intro to solving systems of equations using substitution

<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>


Solving a system of two linear equations using substitution

Simplifying and solving a system with brackets by substitution

Solving a linear system by isolating x and substituting

Solving a system with fractions using substitution for x

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.