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

(i) x₁, the value of x when y = 3.

(ii) y₁, the value of y, when x = 3.

Step 1:

Give at least three suitable values to the variable x and find the corresponding values of y.

Let x = 4, then 4 $\times$ (4) - y = 5 ⇒ y = 11

Let x = 3.5, then 4 $\times$ 3.5 - y = 5 ⇒ y = 9

Let x = 1, then 4 $\times$ 1 - y = 5 ⇒ y = -1

Step 2:

Make a table (as given below) for the different pairs of the values of x and y:

Step 3:

Plot the points, from the table, on a graph paper and then draw a straight line AB passing through the points plotted on the graph.

(i) To find x₁, the value of x, when y = 3:

Through the point y = 3, draw a horizontal straight line which meets the line AB at point C.

Through point C, draw a vertical line which meets the x-axis at x = 2.

Hence, the value of x, when y = 3 is 2 , i.e, x₁ = 2.

(ii) To find y₁, the value of y, when x = 3:

Through the point x = 3, draw a vertical line which meets the line AB at point D.

Through point D, draw a horizontal line which meets the y-axis at y = 7.

Hence, the value of y, when x = 3 is 7 , i.e, y₁ = 7.