Question

Draw the graph of line 4x − y = 5. Use this graph to find:

1. x₁, the value of x when y = 3.
2. y₁, the value of y, when x = 3.

Answer 1

Given:

Equation of the line is 4x − y = 5, with sub-parts to find x₁ when y = 3 and y₁ when x = 3

Formula:

y = 4x − 5

Solution:

4(0) − y = 5 ⇒ y = −5  [Calculating y when x = 0 to find point (0, −5)]

4(1) − y = 5 ⇒ y = −1  [Calculating y when x = 1 to find point (1, −1)]

4(2) − y = 5 ⇒ y = 3  [Calculating y when x = 2 to find point (2, 3)]

4(3) − y = 5 ⇒ y = 7  [Calculating y when x = 3 to find point (3, 7)]

4x₁ − 3 = 5  [Substituting y = 3 into the equation to find x₁]

4x₁ = 8  [Transposing −3 to the right side}]

∴ x₁ = 2  [Dividing both sides by 4 to get x₁]

4(3) − y₁ = 5  [Substituting x = 3 into the equation to find y₁]

12 − y₁ = 5  [Multiplying 4 by 3]

∴ y₁ = 12 − 5 = 7  [Transposing terms to solve for y₁]

∴ x₁ = 2 and y₁ = 7