Question

Solve the following system of equations graphically:

2x + y = 5 and 4x – y = 7. Hence, write the coordinates of the points where given lines meet y-axis.

Answer 1

Step 1: Express y in terms of x

Equation 1: 2x + y = 5

⇒ y = 5 – 2x 

Equation 2: 4x – y = 7

⇒ y = 4x – 7

Step 2: Find points for plotting the lines

To plot the lines, we calculate a few sample points (x, y) for each equation:

For Line 1 (2x + y = 5):

If x = 0, then y = 5 – 2(0) = 5

⇒ (0, 5)   ...(y-intercept) 

If x = 1, then y = 5 – 2(1) = 3

⇒ (1, 3) 

If x = 2, then y = 5 – 2(2) = 1

⇒ (2, 1)

For Line 2 (4x – y = 7): 

If x = 0, then y = 4(0) – 7 = –7

⇒ (0, –7)   ...(y-intercept) 

If x = 2, then y = 4(2) – 7 = 1

⇒ (2, 1)

If x = 3, then y = 4(3) – 7 = 5

⇒ (3, 5)

Graph visualization

Solution of the system: The two lines intersect precisely at (2, 1).

Y-axis intersection points:

The line 2x + y = 5 meets the y-axis at (0, 5). 

The line 4x – y = 7 meets the y-axis at (0, –7).