2.2

Equations

9 flashcards to master Equations

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Key Concept Flip

What is the primary goal when solving an equation?

Answer Flip

The main goal is to isolate the unknown variable (

Example: 'x') on one side of the equation to determine its value. This is achieved by performing the same operations on both sides to maintain balance.
Key Concept Flip

Solve the linear equation: 2x + 5 = 11

Answer Flip

Subtract 5 from both sides: 2x = 6. Then, divide both sides by 2: x = 3. Therefore, the solution is x = 3.

Key Concept Flip

Explain the concept of 'balance' in the context of solving equations.

Answer Flip

The equation must remain equal. Any operation performed on one side of the equation must also be performed on the other side to maintain equality.

Definition Flip

What are 'inverse operations' and why are they important for solving equations?

Answer Flip

Inverse operations are operations that undo each other (

Example: addition and subtraction, multiplication and division). They are crucial for isolating the variable by reversing the operations applied to it.
Definition Flip

Define 'solution' in the context of an equation.

Answer Flip

The solution is the value (or values) of the unknown variable that makes the equation true. Substituting the solution back into the original equation should result in a balanced equation.

Key Concept Flip

Solve for x and y using elimination: x + y = 5, x - y = 1

Answer Flip

Add the two equations: 2x = 6, so x = 3. Substitute x = 3 into the first equation: 3 + y = 5, so y = 2. Therefore, x=3 and y=2.

Definition Flip

Explain the 'substitution' method for solving simultaneous equations.

Answer Flip

Solve one equation for one variable, then substitute that expression into the other equation. This creates a single equation with one variable, which can then be solved. Finally, substitute the solved variable's value back to get the other variable.

Key Concept Flip

When solving the equation 3(x - 2) = 9, what is the first step?

Answer Flip

The first step is to either divide both sides of the equation by 3, or distribute the 3 into the parentheses to get 3x - 6 = 9. Both approaches are valid.

Key Concept Flip

Solve the following: 5x - 3 = 12

Answer Flip

Add 3 to both sides: 5x = 15. Divide both sides by 5: x = 3. Therefore the solution is x = 3.

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2.1 Algebraic notation and manipulation 2.3 Inequalities

Key Questions: Equations

What are 'inverse operations' and why are they important for solving equations?

Inverse operations are operations that undo each other (

Example: addition and subtraction, multiplication and division). They are crucial for isolating the variable by reversing the operations applied to it.
Define 'solution' in the context of an equation.

The solution is the value (or values) of the unknown variable that makes the equation true. Substituting the solution back into the original equation should result in a balanced equation.

Explain the 'substitution' method for solving simultaneous equations.

Solve one equation for one variable, then substitute that expression into the other equation. This creates a single equation with one variable, which can then be solved. Finally, substitute the solved variable's value back to get the other variable.

About Equations (2.2)

These 9 flashcards cover everything you need to know about Equations for your Cambridge IGCSE Mathematics (0580) exam. Each card is designed based on the official syllabus requirements.

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