Concept 1: Linear Equations Linear Relationships Unit Text Reference (Chapter 4.1)

What is a linear relationship? A linear relationship between two variables exist if the graph of the relationship is a linear graph (straight line) A change in one variable (the independent) produces a uniform change in the other (the dependent). A linear relationship is described by a linear equation

Solving linear equations 1. Solving simple linear equations (unknown on one side) 2. Solving linear equations (unknown on both sides) 3. Solving linear equations containing fractions 4. Writing and solving linear equations

1. Solving linear equations (unknown on one side) Example 1: Step 1: Add or subtract the amount not directly attached to the variable (in this case add 6) Step 2: Write the expression again and then divide by the coefficient of x (in this case 5) Step 3: Write the final answer. Check you are correct by substituting back into the original question.

1. Solving linear equations (unknown on one side) Example 1: Step 1: Subtract 6 from both sides Step 2: Divide both sides by -4 Step 3: Write the final answer. Check you are correct by substituting back into the original question.

1. Solving linear equations (unknown on one side) Example 2: Step 1: Subtract 4 from both sides Step 2: Write the expression again and then multiply each side by 2 Step 3: Write the expression again and then divide both sides by 3 Step 4: Write your answer. You can check by substituting back into the original equation to see if you get the correct answer

2. Solving linear equations (unknown on both sides) Before solving this equation we need to first add or subtract a variable term on both sides of the equation so that the variable term appears only on one side of the equation. In this case we subtract 2a from each side. Then solve as in previous examples

2. Solving linear equations (unknown on both sides) Step 1: Expand brackets Step 2: Move variables onto one side (in this case +3k both sides) Step 3: Solve for k

3. Solving linear equations (containing fractions) Step 1: Find the lowest common denominator (in this case 15 which is the first number that appears in both the 5 and 3 times table) Step 2: Write the equation using the lowest common denominator (LCD) Step 3: Multiply both sides by the LCD (this gets rid of the denominators) Step 4: Expand the brackets Step 5: Simplify so variables on one side (in this case subtract 3x from both sides Step 6: Solve for x

4. Writing and solving equations The sum of three consecutive numbers is 21. Find the unknown numbers. Step One: DEFINE Let the first number be x Let the second number be x+1 Let the third number be x+2 Step Two: WRITE THE EQUATION x + (x + 1) + (x + 2) = 21 Step Three: SOLVE THE EQUATION 3x + 3 = 21 3x = 18 x = 6 Step Four: ANSWER THE QUESTION The three consecutive numbers that add to 21 are 6,7 and 8.

Checklist Have I updated my summary book? Do I understand how to do the following? 1. Solving simple linear equations (unknown on one side) 2. Solving linear equations (unknown on both sides) 3. Solving linear equations containing fractions 4. Writing and solving linear equations Exercise 4.1 I have completed at least Fluency: 5 questions from each of Q1,Q2,Q3 and Q4 Understanding: 4 questions from Q7,Q8,Q9,Q10,Q11,Q12,Q13,Q14,Q15 Reasoning: Question 16 or Question 17