Linear Equations
Solving one linear equation, solving a pair by substitution and elimination, forming equations from word problems, and recognising when a pair has one solution, none, or infinitely many.
What you will be able to do
- Solve a linear equation in one variable, clearing brackets and fractions first.
- Solve a pair of linear equations by substitution and by elimination.
- Translate an age, coin or two-digit-number problem into a pair of equations.
- Decide from the coefficients whether a pair has one, no, or infinitely many solutions.
What is inside this lesson
- 1What linear means
- 2One equation, one variable
- 3Two variables: substitution and elimination
- 4Turning a word problem into equations
- 5One solution, none, or infinitely many
- 6Worked examples
- 7Common mistakes
- 8Quick revision
- 9Practice
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What linear means
An equation is linear when every variable appears only to the first power, with no products of variables and nothing under a root. So 3x minus 5 equals 7 is linear; x^2 equals 9 and xy equals 6 are not.
In the exam, linear equations turn up in two shapes. One is a bare equation or pair of equations to solve. The other, more common, is a word problem about ages, coins, marks, a two-digit number, or a break-even quantity, where the real work is setting up the equations. Both are covered here.
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