Question

Solve graphically:

x – 2y = 1, x + 2y = 5

Answer 1

To solve the system of linear equations graphically:

x – 2y = 1

x + 2y = 5

Step 1: Find points for each line

For each equation, find two points by substituting convenient values for x or y.

For x – 2y = 1:

If x = 1: 1 – 2y = 1

⇒ –2y = 0

⇒ y = 0

Point: (1, 0)

If x = 3: 3 – 2y = 1

⇒ –2y = –2

⇒ y = 1

Point: (3, 1)

For x + 2y = 5:

If x = 5: 5 + 2y = 5

⇒ 2y = 0

⇒ y = 0

Point: (5, 0)

If x = 3: 3 + 2y = 5

⇒ 2y = 2

⇒ y = 1

Point: (3, 1)

Step 2: Plot the lines on a graph

Draw a coordinate plane and plot the points found above.

Draw a straight line passing through (1, 0) and (3, 1) for the first equation.

Draw another straight line passing through (5, 0) and (3, 1) for the second equation.

Step 3: Identify the intersection point

The point where the two lines cross is the solution to the system. From the graph, both lines intersect at the point (3, 1).