Year 7 Maths: Find a Value Using Two-Variable Equations

Introduction to Two-Variable Equations

Hello, Year 7! Today, we’re going to learn about two-variable equations. These are equations that involve two different variables, usually represented by letters like (x) and (y).

What is a Two-Variable Equation?

A two-variable equation looks like this:

$$

y = 2x + 3

$$

In this equation, (y) depends on (x). This means whenever we choose a value for (x), we can find a corresponding value for (y).

How to Find a Value

To find a value using a two-variable equation, follow these steps:

1. Choose a value for one variable.
2. Substitute that value into the equation.
3. Calculate the value of the other variable.

Example

Let’s say we have the equation:

$$

y = 2x + 1

$$

1. Choose a value for (x): Let’s pick (x = 2).
2. Substitute into the equation:$$y = 2(2) + 1$$
3. Calculate (y):$$y = 4 + 1 = 5$$

So, when (x = 2), (y = 5).

Key Rules

• Always substitute carefully.
• Perform the calculations step-by-step.
• You can pick any value for (x) or (y) to find the other.

Tips and Tricks

• Start with easy numbers like 0 or 1 to practice.
• Check your work by substituting back into the original equation.
• Remember that one equation can have many pairs of (x) and (y).

Practice Questions

Easy Level Questions

1. If (y = 3x + 2), find (y) when (x = 1).
2. If (y = 2x – 4), find (y) when (x = 0).
3. If (y = x + 5), find (y) when (x = 3).
4. If (y = 4x), find (y) when (x = 2).
5. If (y = x – 1), find (y) when (x = 5).
6. If (y = 2x + 3), find (y) when (x = 4).
7. If (y = 5x), find (y) when (x = 1).
8. If (y = x + 2), find (y) when (x = 0).
9. If (y = 6x – 1), find (y) when (x = 2).
10. If (y = 7 – x), find (y) when (x = 3).
11. If (y = 3x + 1), find (y) when (x = 2).
12. If (y = 4 – x), find (y) when (x = 2).
13. If (y = 2x), find (y) when (x = 5).
14. If (y = x + 3), find (y) when (x = 1).
15. If (y = 10 – 2x), find (y) when (x = 4).
16. If (y = 8x + 1), find (y) when (x = 0).
17. If (y = x + 4), find (y) when (x = 2).
18. If (y = 5 – x), find (y) when (x = 1).
19. If (y = 3x – 5), find (y) when (x = 3).
20. If (y = 2x + 2), find (y) when (x = 1).

Medium Level Questions

1. If (y = 2x + 5), find (y) when (x = 3).
2. If (y = 3x – 2), find (y) when (x = 4).
3. If (y = 4 – 3x), find (y) when (x = 1).
4. If (y = 5 + 2x), find (y) when (x = 2).
5. If (y = 7x + 1), find (y) when (x = 0).
6. If (y = 6 – 2x), find (y) when (x = 3).
7. If (y = 4x + 4), find (y) when (x = 5).
8. If (y = 3 – x), find (y) when (x = 2).
9. If (y = 8x – 3), find (y) when (x = 1).
10. If (y = x^2 + 2), find (y) when (x = 2).
11. If (y = 2x^2 – 4), find (y) when (x = 2).
12. If (y = 5 – x^2), find (y) when (x = 1).
13. If (y = 10 + 3x), find (y) when (x = 0).
14. If (y = 2 – 4x), find (y) when (x = 1).
15. If (y = 1 + 5x), find (y) when (x = 3).
16. If (y = x/2 + 5), find (y) when (x = 6).
17. If (y = 9 – 2x), find (y) when (x = 4).
18. If (y = 4 + 3x), find (y) when (x = 0).
19. If (y = 7 – x^2), find (y) when (x = 3).
20. If (y = 2x + 6), find (y) when (x = 5).

Hard Level Questions

1. If (y = 3x^2 – 2x + 1), find (y) when (x = 2).
2. If (y = 5 – x^2 + 3x), find (y) when (x = 1).
3. If (y = 4x^2 – 3x + 2), find (y) when (x = 3).
4. If (y = x^2 + 5x – 6), find (y) when (x = -1).
5. If (y = 2x^2 + x + 4), find (y) when (x = 2).
6. If (y = 3x^2 – 4x + 1), find (y) when (x = 1).
7. If (y = 5x – x^2 + 4), find (y) when (x = 3).
8. If (y = 6 – x^2 + 2x), find (y) when (x = 2).
9. If (y = 2x + 3x^2 – 1), find (y) when (x = 1).
10. If (y = 4x^2 + 3x – 2), find (y) when (x = -1).
11. If (y = 7 – 2x^2 + 5x), find (y) when (x = 1).
12. If (y = -x^2 + 6x – 5), find (y) when (x = 2).
13. If (y = 3x^2 – 5x + 2), find (y) when (x = 3).
14. If (y = 2 + 3x – 4x^2), find (y) when (x = 1).
15. If (y = x^2 – 2x + 5), find (y) when (x = 3).
16. If (y = 5x + x^2 – 3), find (y) when (x = 2).
17. If (y = 4x – 3x^2), find (y) when (x = 1).
18. If (y = 2x^2 + 3 – x), find (y) when (x = 4).
19. If (y = -x^2 + 4x + 1), find (y) when (x = 5).
20. If (y = x^2 – 1 + 3x), find (y) when (x = -2).

Answers and Explanations

Easy Level Answers

1. (y = 3(1) + 2 = 3 + 2 = 5)
2. (y = 2(0) – 4 = 0 – 4 = -4)
3. (y = 3 + 5 = 8)
4. (y = 4(2) = 8)
5. (y = 5 – 1 = 4)
6. (y = 2(4) + 3 = 8 + 3 = 11)
7. (y = 5(1) = 5)
8. (y = 0 + 2 = 2)
9. (y = 6(2) – 1 = 12 – 1 = 11)
10. (y = 7 – 3 = 4)
11. (y = 3(2) + 1 = 6 + 1 = 7)
12. (y = 4 – 2 = 2)
13. (y = 2(5) = 10)
14. (y = 1 + 3 = 4)
15. (y = 10 – 8 = 2)
16. (y = 8 + 1 = 9)
17. (y = 5 – 1 = 4)
18. (y = 2 + 3x = 2 + 12 = 14)
19. (y = -9 + 20 + 1 = 12)
20. (y = 2 + 3 = 5)

Medium Level Answers

1. (y = 2(3) + 5 = 6 + 5 = 11)
2. (y = 3(4) – 2 = 12 – 2 = 10)
3. (y = 4 – 3(1) = 4 – 3 = 1)
4. (y = 5 + 2(2) = 5 + 4 = 9)
5. (y = 0 + 1 = 1)
6. (y = 6 – 2(3) = 6 – 6 = 0)
7. (y = 4(5) + 4 = 20 + 4 = 24)
8. (y = 3 – 2 = 1)
9. (y = 8(1) – 3 = 8 – 3 = 5)
10. (y = 4 + 8 – 6 = 6)
11. (y = 2(2)^2 – 4 = 8 – 4 = 4)
12. (y = 5 – 1 = 4)
13. (y = 10 + 0 = 10)
14. (y = 1 – 4 = -3)
15. (y = 1 + 15 = 16)
16. (y = 3 – 12 + 2 = -7)
17. (y = 4 + 0 = 4)
18. (y = 4 + 3 = 7)
19. (y = 7 – 9 = -2)
20. (y = 10 + 12 = 22)

Hard Level Answers

1. (y = 3(2)^2 – 2(2) + 1 = 12 – 4 + 1 = 9)
2. (y = 5 – 1 + 3 = 7)
3. (y = 4(3)^2 – 3(3) + 2 = 36 – 9 + 2 = 29)
4. (y = 1 + 5 – 6 = 0)
5. (y = 2(2)^2 + 2 + 4 = 8 + 2 + 4 = 14)
6. (y = 3(1)^2 – 4(1) + 1 = 3 – 4 + 1 = 0)
7. (y = 5(3) – (3^2) + 4 = 15 – 9 + 4 = 10)
8. (y = 6 – 4 + 4 = 6)
9. (y = 2(1) + 3(1)^2 – 1 = 2 + 3 – 1 = 4)
10. (y = 4(-1)^2 + 3(-1) – 2 = 4 – 3 – 2 = -1)
11. (y = 7 – 2(-1)^2 + 5(-1) = 7 – 2 – 5 = 0)
12. (y = -(-2)^2 + 6(-2) – 5 = -4 – 12 – 5 = -21)
13. (y = 3(3)^2 – 5(3) + 2 = 27 – 15 + 2 = 14)
14. (y = 2 + 3(1) – 4(1)^2 = 2 + 3 – 4 = 1)
15. (y = 9 – 6 + 5 = 8)
16. (y = 4(1) – 3(1^2) = 4 – 3 = 1)
17. (y = 2(4^2) + 3 – 4 = 32 + 3 – 4 = 31)
18. (y = -2^2 + 4(-2) + 1 = -4 – 8 + 1 = -11)
19. (y = -5^2 + 20 – 3 = -25 + 20 – 3 = -8)
20. (y = (-2)^2 – 1 + 3(-2) = 4 – 1 – 6 = -3)

I hope this helps you understand how to find values using two-variable equations! Keep practicing, and you’ll get even better!