#Solvingequationsinvolvingindices

For a complete lesson on solving polynomial equations, go to https://www.MathHelp.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn that the first step in solving polynomial equations is to set the given equation equal to zero, the next step is to factor, and the final step is to set each of the resulting factors equal to zero and solve each equation. This process usually yields more than one solution, so the answer can be written as a solution set. Some of the problems involve factoring a trinomial into two binomials, and some of the problems involve factoring a binomial as the difference of two squares.

This video demonstrates how to solve a linear equation that contains fractions by multiplying each term by the LCD. This video was created for my community college introductory algebra class.

How to solve equations with brackets or parenthesis using distributive method or another method.

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Solving Two-Step Equations | Expressions & Equations | Grade 7

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Goal: Solve equations by balancing.

MIT grad shows how to use the elimination method to solve a system of linear equations (aka. simultaneous equations). To skip ahead: 1) For a BASIC example where terms cancel right away when you add the equations, skip to 0:25. 2) For an example in which you have to MULTIPLY ONE EQUATION by a number before adding the equations, skip to time 6:26. 3) For an example in which you have to MULTIPLY BOTH EQUATIONS by numbers before adding, skip to 12:12. P.S.) For HOW TO SUBTRACT equations instead of adding them, if you'd rather do that, skip to 18:00. Nancy formerly of MathBFF explains the steps.

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For how to solve a system of linear equations by the SUBSTITUTION METHOD, jump to: https://youtu.be/YriMMWbndn0

What does it mean to solve a system of equations using the elimination method? It means to solve for the x and y values that make both equations true, using the elimination method. Elimination is just one way of solving (substitution is another way) and is sometimes called linear combination. Here's how:

1) BASIC ELIMINATION: First, make sure the equations are ordered in the same way, with their like terms lined up vertically. Then, try adding the equations (vertically) to make a new equation. If a term in the first equation has the same number coefficient but opposite sign (like 5y and -5y), then adding the equations will mean that those terms cancel. Since those terms disappear (in the example, 5y and -5y), there is just the variable x left in the equation so you can solve for x. Once you solve for x, you can take that number and plug it in for x in either of the original equations in the system, to solve for the other variable, y. The (x,y) pair is your solution.

2) MULTIPLY ONE EQUATION BEFORE ADDING: Sometimes terms don't immediately cancel when you add the two equations. What do you do then? Try multiplying one of the equations by a number (both the left and right sides) to make either the x terms or y terms have similar coefficients (but opposite sign), like positive 4x and negative 4x. Then add the two equations (the new version) and follow the same steps as in the first example.

3) MULTIPLY BOTH EQUATIONS BEFORE ADDING: If it does not help to just multiply one equation by a number, you may need to multiply both equations, separately, by numbers. If you check to see whether you can just multiply one equation by a number and add opposite terms/eliminate a variable, and it is not possible, then aim for an LCM, or least common multiple, by multiplying each equation by a different number, and then adding the equations.

P.S.) YES, YOU CAN SUBTRACT INSTEAD (if you want): If you have a system that has the exact same x terms or exact same y terms in both equations, if you prefer, you can just subtract the equations. Alternatively, if you still wanted to add the equations, you could just multiply one of the equations by -1 first and then add the equations and solve normally.

IMPORTANT: If you get something like 0 = 0 or 8 = 8, or something like 1 = 2 or 0 = 21 when you are following these steps and trying to solve, then you have probably found a special case. If you get something TRUE like 0 = 0 (a number equals the same number), then there are an infinite number of solutions to the system, and you can just write "infinitely-many solutions". If instead you get something FALSE like 0 = 21, then there is no solution (inconsistent system), and you can write "no solution".

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Learn 5 Methods for solving quadratic equations in this video math tutorial by Mario's Math Tutoring. We discuss the graphing, factoring, quadratic formula, completing the square, and the taking square roots methods and go through 1 example of each type in this video.

Related Videos to Help You Succeed!:

Graphing Parabolas:
https://youtu.be/HBVevKX0_5w

Solving a Quadratic Equation by Completing the Square
https://youtu.be/w7NqpGqyq5Q

Quadratic Formula
https://youtu.be/OmxdT5RzMq0

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This algebra video tutorial explains how to solve quadratic equations by completing the square. Here are some other youtube videos with more example problems:

How To Solve Simple Quadratic Equations: https://www.youtube.com/watch?v=-KWsS2FZVTA

Solving Quadratic Equations By Factoring:
https://www.youtube.com/watch?v=qeByhTF8WEw

How To Factor Difficult Quadratic Equations:
https://www.youtube.com/watch?v=VG1luiL_INQ

Solving QE By Completing The Square:
https://www.youtube.com/watch?v=WOb25i8FBBw

Solving Equations In Quadratic Form:
https://www.youtube.com/watch?v=eWjixwGK3YM

Sum and Products - Quadratic Equations:
https://www.youtube.com/watch?v=kBSj35rik8w

_______________________________________
How To Calculate The Discriminant:
https://www.youtube.com/watch?v=6fU9ZgwbU74

Standard Form to Vertex Form:
https://www.youtube.com/watch?v=pf9LkX8hpTQ

Graphing Quadratic Functions:
https://www.youtube.com/watch?v=H8OQtxSRe_k

How To Find The Axis of Symmetry:
https://www.youtube.com/watch?v=tyzd4VujaqY

Graphing Quadratic Functions - Vertex Form:
https://www.youtube.com/watch?v=OHH7fX_M8Ns

Graphing QF in Standard Form:
https://www.youtube.com/watch?v=uYNKJWFYh7k

___________________________________________
Writing Quadratic Equations:
https://www.youtube.com/watch?v=SB6eCyG4GEA

Maximum and Minimum Word Problems:
https://www.youtube.com/watch?v=d5YktqR-4FU

Systems of Quadratic Equations:
https://www.youtube.com/watch?v=rq5AjFs95qw

Systems of Nonlinear Equations:
https://www.youtube.com/watch?v=JPdLEaxlnZQ

Quadratic Inequalities:
https://www.youtube.com/watch?v=_gWjLKsFOPE

Quadratic Equations - Test Review:
https://www.youtube.com/watch?v=fFFA7Q4eVuY

___________________________________________
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Corbettmaths - This video goes through how to solve equations that involve algebraic fractions.

A video revising the techniques and strategies for solving simultaneous equations.

This video is part of the Algebra module in GCSE maths, see my other videos below to continue with the series.

These are the calculators that I recommend:

Casio fx-83GTX Scientific Calculator, Black - https://amzn.to/2P2cyGG
Casio Fx-991ex Scientific Calculator Fx 991 Ex - New + 552 Function - Classwiz - https://amzn.to/2sw2Moz

🔹 Watch the video
🔹 Make notes
🔹 Practice the questions
🔹 Mark your work
🔹 Review what you have learnt on the exam questions

Part 1 - Laws of Indices - https://youtu.be/cu2pvWTtQQI

Part 2 - Collecting Like Terms - https://youtu.be/r0R33BtNP44

Part 3 - Expanding and Simplifying - https://youtu.be/WUXCFtL5G3U

Part 4 - Double Brackets - https://youtu.be/Bhjo0x5ow5k

Part 5 - Factorising - https://youtu.be/yIShSwge8bw

Part 6 - Factorising Quadratics - https://youtu.be/CPzWzl3U5Gg

Part 7 - Substitution - https://youtu.be/oGFLF_mpXH8

Part 8 - Changing the Subject Part 1 - https://youtu.be/QmBmzE5PnyA

Part 9 - Simultaneous Equations - https://youtu.be/2jrgXG0XsCc

Part 10 - Changing the Subject Part 2 (Higher Only) - https://youtu.be/ugcR-khcTLQ

Part 11 - Expanding Triple Brackets (Higher Only) - https://youtu.be/s86OeEtLHj8

Part 12 - Factorising Harder Quadratics (Higher Only) - https://youtu.be/DEoeiFTODAU

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Solving Quadratic Equations by Factoring - Basic Examples. In this video, I solve two basic quadratic equations by factoring.

✅CHECK YOUR ANSWERS✅

ON YOUR OWN ANSWERS
1) a = 48
2) y = 35
3) z = 6
4) p = 6
5) q = 5
6) r = 9
7) 5t = 70
t = 14, so each ticket costs $14

This video is about how to solve one-variable equations using either multiplication or division. We discuss the basic principles of equations and how to solve them conceptually. From there, we do a lot of practice problems solving one-step equations.

In this video I show you how to solve equations involving surds. Surd equations have a square root in them and the method we use to solve these is to isolate the square root and then square both sides. This may need to be done a number of times depending on how many surds are in the equation.

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Kevin MacLeod: Carefree
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👉Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be equal in all the equations that make up the system, in order to eliminate the variable using subtraction (or addition as the case may be). The coefficients can be made equal by multiplying the entire equation with a number which when multiplied to the coefficient of the variable to be eliminated gives the LCM of the coefficients of the variable to be eliminated in all the equations. Then we solve for the remaining variable(s).

After we have obtained the solution{s} for the remaining variable(s), we substitute the obtained solution into any of the original equations to obtain the solution of the eliminated variable.

✅ Solve a System of Three Equations - https://youtu.be/nLar40Dd_Us

00:00 intro
1:44 Multiply each equation
2:30 Add both equations
2:53 Solve for y

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✅Solve a System of Equations Using Substitution | Easy
https://www.youtube.com/playli....st?list=PL0G-Nd0V5ZM
✅Solve a System of Equations Using Substitution | Hard
https://www.youtube.com/playli....st?list=PL0G-Nd0V5ZM
✅Solve a System of Equations Using Substitution | Learn About
https://www.youtube.com/playli....st?list=PL0G-Nd0V5ZM
✅Solve a System of Equations Using Elimination | Learn About
https://www.youtube.com/playli....st?list=PL0G-Nd0V5ZM
✅Solve a System of Equations Using Elimination | Easy
https://www.youtube.com/playli....st?list=PL0G-Nd0V5ZM
✅Solve a System of Equations Using Elimination | Medium
https://www.youtube.com/playli....st?list=PL0G-Nd0V5ZM
✅Solve a System of Equations Using Elimination | Hard
https://www.youtube.com/playli....st?list=PL0G-Nd0V5ZM
✅Solve a System of Equations Word Problem
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How to solve this equation? By using this trick, you can deal it quickly!

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Remember that what you do to one side, you have to do to the other. Will you multiply or divide both sides to dump the fraction, x/a? Let's do it together.

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/equations_beginner/e/linear_equations_1?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI

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Missed the previous lesson?
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Algebra I on Khan Academy: Algebra is the language through which we describe patterns. Think of it as a shorthand, of sorts. As opposed to having to do something over and over again, algebra gives you a simple way to express that repetitive process. It's also seen as a "gatekeeper" subject. Once you achieve an understanding of algebra, the higher-level math subjects become accessible to you. Without it, it's impossible to move forward. It's used by people with lots of different jobs, like carpentry, engineering, and fashion design. In these tutorials, we'll cover a lot of ground. Some of the topics include linear equations, linear inequalities, linear functions, systems of equations, factoring expressions, quadratic expressions, exponents, functions, and ratios.

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