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PROGRAMME F5. LINEAR EQUATIONS and SIMULTANEOUS LINEAR EQUATIONS. Programme F5: Linear equations and simultaneous linear equations. Linear equations Simultaneous linear equations with two unknowns Simultaneous linear equations with three unknowns.

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PROGRAMME F5

LINEAR EQUATIONS and

SIMULTANEOUS LINEAR EQUATIONS


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Programme F5: Linear equations and simultaneous linear equations

Linear equations

Simultaneous linear equations with two unknowns

Simultaneous linear equations with three unknowns


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Programme F5: Linear equations and simultaneous linear equations

Linear equations

Simultaneous linear equations with two unknowns

Simultaneous linear equations with three unknowns


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Programme F5: Linear equations and simultaneous linear equations

Linear equations

Solution of simple equations

A linear equation in a single variable (unknown) involves powers of the variable no higher than the first. A linear equation is also referred to as a simple equation.

The solution of simple equations consists essentially of simplifying the expressions on each side of the equation to obtain an equation of the form:


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Programme F5: Linear equations and simultaneous linear equations

Linear equations

Simultaneous linear equations with two unknowns

Simultaneous linear equations with three unknowns


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Programme F5: Linear equations and simultaneous linear equations

Simultaneous linear equations with two unknowns

Solution by substitution

Solution by equating coefficients


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Programme F5: Linear equations and simultaneous linear equations

Simultaneous linear equations with two unknowns

Solution by substitution

A linear equation in two variables has an infinite number of solutions. For two such equations there may be just one pair of x- and y-values that satisfy both simultaneously. For example:


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Programme F5: Linear equations and simultaneous linear equations

Simultaneous linear equations with two unknowns

Solution by equating coefficients

Example:

Multiply (a) by 3 (the coefficient of y in (b)) and multiply (b) by 2 (the coefficient of y in (a))


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Programme F5: Linear equations and simultaneous linear equations

Linear equations

Simultaneous linear equations with two unknowns

Simultaneous linear equations with three unknowns


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Programme F5: Linear equations and simultaneous linear equations

Simultaneous linear equations with three unknowns

With three unknowns and three equations the method of solution is just an extension of the work with two unknowns.

By equating the coefficients of one of the variables it can be eliminated to give two equations in two unknowns. These can be solved in the usual manner and the value of the third variable evaluated by substitution.


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Programme F5: Linear equations and simultaneous linear equations

Simultaneous linear equations

Pre-simplification

Sometimes, the given equations need to be simplified before the method of solution can be carried out. For example, to solve:

Simplification yields:


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Programme F5: Linear equations and simultaneous linear equations

Learning outcomes

  • Solve any linear equation

  • Solve simultaneous linear equations in two unknowns

  • Solve simultaneous linear equations in three unknowns


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