Linear equations
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Equations in general
Equation means equality for two expressions. An equation is equivalent with the original equation, if
- the same number is added for both sides of the equation,
- the same number is subtracted from both sides of the equation,
- both sides are multiplied or divided with the same number which is NOT zero.
Standard form:
where x is the variable and a and b are parameters (values unknown but constant). The solution (the root of equation) is
where . If a = 0 and b = 0, then any value of satisfies the equation (identically true).
If a = 0 and , the equation has no root (identically false).
Solving linear equations
- Remove all brackets and denominators.
- Transpose the equation so that terms with variable are in one side of the equation and constants are on the other side.
- Combine like terms for to get the equation into a form ax = b.
- Divide by the multiplier of the variable.
- Check the root by substituting it to the original equation.