Question

Solve the following system of equations graphically:

2x + 3y = 6

x + y – 1 = 0

Also, find the sum of ordinates of the points where given lines meet y-axis.

Answer 1

Step 1: Find points for each line

To plot the linear equations, we determine at least two points for each line by finding their intercepts.

For Line 1: 2x + 3y = 6

x = 0

⇒ 3y = 6 

⇒ y = 2

Point is (0, 2). 

y = 0

⇒ 2x = 6 

⇒ x = 3

Point is (3, 0).

For Line 2: x + y – 1 = 0

⇒ x + y = 1 

x = 0 ⇒ y = 1

Point is (0, 1). 

y = 0 ⇒ x = 1

Point is (1, 0).

Step 2: Graphical representation

Plotting these coordinates and drawing straight lines through them gives the following graph:

As observed from the graph, the two lines intersect precisely at the point (–3, 4).

Therefore, the solution to the system of equations is x = –3 and y = 4.

Step 3: Sum of ordinates on the y-axis

The ordinate refers to the y-coordinate of a point. The lines meet the y-axis at points where x = 0.

Line 1 meets the y-axis at (0, 2), so its ordinate is 2.

Line 2 meets the y-axis at (0, 1), so its ordinate is 1.

Sum of ordinates = 2 + 1 = 3