Equations Worksheets and Answers
Equations Worksheet Practice
Equations worksheets for year 7, year 8, year 9, year 10 and year 11. Equations worksheet 1, equations worksheet 2 and equations worksheet 3 are forming and solving exercises for gcse foundation and gcse higher. Equations worksheet 4 is a I think of a number exercise. Equations worksheet 5 involves a 15 minute solving equations challenge. Equations worksheet 6 involves solving equations using area of rectangles. Equations worksheet 7 and Equations worksheet 8 are traditional equation worksheets. Equations worksheet 9 asks students to solve equations involving algebraic perimeters. Equations worksheet 10, Equations worksheet 11 and Equations worksheet 12 work at grade 2, grade 3 and grade 4 respectively. Equations worksheet 10, Equations worksheet 11 and Equations worksheet 12 involve solving equations with brackets as well as solving equations involving fractions. Equations worksheet 13, Equations worksheet 14, Equations worksheet 15, Equations worksheet 16 and Equations worksheet 17 involve solving quadratic equations including the difference of two squares and the quadratic formula. Equations worksheet 18, Equations worksheet 19, Equations worksheet 20 and Equations worksheet 23 asks students to solve simultaneous equations including use of the graphical method. Equations worksheet 21 and Equations worksheet 22 asks students to use trial and error in order to solve the equations given. Equations worksheet 24 works at grade 3 and it excludes all possibility of students working with negative numbers. Equations worksheet 25 focuses on the completing the square method and has been added later on as an addition to the other Equations worksheets.
What Are Linear Equations?
Students learn how to solve equations from year 7 onward. Solving equations ranges in difficulty. Students may understand how to manipulate algebraic expressions before they are ready to solve equations.
Linear Equations Example 1
The image below shows different examples of linear equations.
2c = 4 is different to x - 5 = -1. With the equation 2c = 4 we divide both sides by 2. The answer is c = 2. With x - 5 = -1 we add (-5) to both sides. The answer is x = 4 because -1 + (-5) equals 4.
Linear Equations Example 2
The linear equation examples below are more tricky.
To solve the equation 2a + 2 - 4a = - 6, we first collect like terms. 2a - 4a is -2a. The equation becomes 2 - 2a = - 6. Next we subtract 2 from both sides. The equation becomes - 2a = - 8. Next we divide both sides by negative 2. We are left with an answer of a = 4.
Linear Equations Example 3
The equations below involve division and or fractions. In the case of 4v / 5 = 8 we first multiply both sides by 5. Next we divide both sides by 4. The final answer is v = 10. We can always substitute the final answer into the original equation to see if it is correct.
How to Solve Linear Equations
Equations is a GCSE Foundation and GCSE Higher topic. Experienced teachers will have their own unique approach when teaching how to solve equations. We recommend the balancing method as this is a common way to introduce the topic solving equations. As prerequisite topics we suggest: simplifying expressions, or substituting into expressions.
Balancing Method vs Function Machine Method
The image below shows an example of the balancing method as well as the function machine method. The equation 8a - 5 = 11 has been solved using the balancing method and the function machine method. a is the subject of the equation.
The final answer is a = 2.
In the example below the equation 10 + 6y = 34 has been solved using the balancing method and the function machine method. y is the subject of the equation.
The final answer is y = 4.
In the example below the equation x/12 - 5 =4 has been solved using the balancing method and the function machine method. x is the subject of the equation.
The final answer is x = 108.
Equations Questions And Answers
For questions on solving quadratic equations try: Solving Quadratic Equations Worksheets. For solving simultaneous equations try: Solving Simultaneous Equations Worksheets. For questions on trial and error try: Trial and Improvement Worksheets.