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Listed under:  Mathematics  >  Algebra  >  Equations
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Substitution in algebra

Substitution is when you replace one thing with something else. In algebra, this often means replacing a letter with a given number in order to work out an equation. Using the substitutes given in this video, see if you can work out the equation a+b (l-mn).

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Algebra: a piece of cake

Can you write an algebraic equation to relate two variables? See how to write an equation that shows how the number of cakes relates to the cake ingredients of eggs, butter, cocoa, flour, sugar and milk.

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A slice of algebra

Do you know how to write an algebraic equation? In this example we use trays of coconut slice. Find out what the equation looks like after a piece of slice from one tray has been eaten. See how this equation can be used to predict the number of slices to be made.


Graphing functions

This collection contains five digital curriculum resources (all interactive learning objects) that introduce students to graphing linear, parabolic, cubic and trigonometric functions. Through exercises, students investigate how the constants in each function equation influence relevant aspects of graphing, such as dilations ...


BBC Bitesize: inequalities and simultaneous equations - revision

These illustrated information sheets review inequality symbols, the representation of inequalities on a number line and the solution of inequalities with a positive coefficient of the unknown. Simultaneous equations are defined and simple pairs of equations are solved using substitution, algebra and graphical representation. ...

Teacher resource

Applications of differentiation

This is a teacher resource for applications of differentiation consisting of a website and a PDF with identical content. It contains a discussion of graph sketching, related rates of change and the solution of maxima and minima questions.

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The language of algebra

Have you seen mathematical expressions that use numbers and letters? They're called algebraic expressions. See what all this means. Watch how you can substitute a value for 'x' in an algebraic expression. It's easy when you know how!

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The key to finding 'y' is 'x'

Try these two exercises, which require you to substitute values of x into an algebraic equation. Complete the table of values for y for both equations.

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Show just how pro numerals you can be!

How do you change a mathematical rule or expression into an equation? See how to write an equation for an expression that has an input (x) and an output (y). See how to write equations that contain division as well as multiplication. Try and find the outputs to these equations by substituting values for x.

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Linear simultaneous equations: elimination

One method of solving linear simultaneous equations is by eliminating either x or y. Start with a straightforward example eliminating one unknown value. In the next example, unknown values x and y are numerically different for each equation. See how you use both elimination and a bit of substituting to find your answer. ...

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Two unknowns: two equations

A written mathematical problem that has two unknowns can be solved using simultaneous equations. See how it's done. The first step is to write the problem as two equations. In these two examples, the equations are linear. The first can be solved using the elimination method. Find out how to set the next two linear equations ...

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Solving linear simultaneous equations graphically

Linear simultaneous equations can be solved graphically. All you need to do is graph each equation and find the x and y coordinates where they intersect. Then just write these as values for x and y. Watch how it's done. You'll be an expert in no time!

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Linear simultaneous equations and substitution

Do you know how to solve linear simultaneous equations by finding values for x and y? Find out about the substitution method in this clip. See how to rewrite and rearrange one of the linear equations to get a value for x or y. Substitute this value into the second equation. Follow the steps and you'll get a number value ...

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Simplifying algebraic fractions

Learn to simplify algebraic fractions using these great tips. Remember your laws of indices, and make sure you look for multiples in order to cancel the numerators and denominators.

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Algebraic fractions

Algebraic fractions are not too different from numerical fractions. In order to add, subtract, multiply and divide them, you need to follow the same rules. Watch this helpful maths video to see how to solve equations using algebraic fractions.

Interactive resource

The take-away bar: generate hard subtractions

Solve subtractions such as 87-29. Use a linear partitioning tool to help solve randomly generated subtractions. Learn strategies to do complex arithmetic in your head. Split a subtraction into parts that are easy to work with, work out each part and then solve the original calculation. This learning object is one in a series ...

Interactive resource

EagleCat: cubic-G

Explore the graphs of cubic equations in two forms: (a) the general form, y = a(x – h)³ + k, and (b) the intercept form, y = (x – a)(x – b)(x – c). Observe changes to the point of inflexion and the shape of cubic graphs through various transformations. Alternately, change the equation and observe changes in the x-intercepts ...

Interactive resource

EagleCat: trig-G

Explore the graphs of trigonometric equations in the form: (a) y = a sin[n(x - h)] + k, (b) y = a cos[n(x - h)] + k and (c) y = a tan[n(x - h)] + k. Use sliders or enter values to dilate, reflect and translate the basic trigonometric equations y = sin(x), y = cos(x) and y = tan(x), and observe the changes in the amplitude, ...

Interactive resource

The take-away bar: go figure

This tutorial is suitable for use with a screen reader. It explains strategies for solving subtractions in your head such as 87-39. Work through sample questions and instructions explaining how to use linear partitioning techniques. Solve subtractions by breaking them up into parts that are easy to work with, work out each ...

Interactive resource

Filling glasses: find the right graph

Look closely at some line graphs. Examine the relationship between the shape of a glass and the time taken to fill it with juice. Notice that the fluid level rises more quickly in a narrow glass than in a wide glass. Choose both sections of a line graph representing the filling rate for a glass shape. This learning object ...