Letters stand for numbers
In algebra a letter such as stands for a number we do not know yet, or for a number that can change. means . An expression like has no equals sign. An equation like says two things are equal.
Worked exampleSimplify an expression
Simplify .
- Group the like terms.
- Combine.
Answer:
Solving equations with one unknown
An equation is like a balance. Whatever you do to one side you must do to the other, so it stays level. Your aim is to get the letter alone.
Try itTest a guess on the balance
Solve . Try values of : when the two sides are equal the balance is level and you have found the answer.
Worked exampleSolve an equation
Solve .
- Add 4 to both sides.
- Divide both sides by 3.
- Check: . ✓
Answer:
Two unknowns
When there are two unknowns you need two equations. Add or subtract the equations to remove one letter, then solve for the other.
Worked exampleSimultaneous equations
Solve and .
- Add the two equations. The terms cancel.
- So .
- Put in the first equation.
Answer: and .
Key terms
- Expression
- Numbers and letters joined by operations, with no equals sign.
- Equation
- A statement that two expressions are equal.
- Like terms
- Terms with the same letter part.
- Simultaneous equations
- Two equations solved together for two unknowns.
Summary
- Only like terms can be added or subtracted.
- Do the same to both sides of an equation to keep it balanced.
- Undo operations in reverse order: add or subtract first, then multiply or divide.
- Two unknowns need two equations: add or subtract to remove one letter.