Question

Solve graphically:

x – y = 0, 2x + y = 6

Answer 1

To solve the given system of equations graphically:

x – y = 0

2x + y = 6

1. Rearrange equations for plotting

We rewrite each equation in the form y = mx + c:

Equation 1:

 x – y = 0

⇒ y = x

Equation 2:

2x + y = 6

⇒ y = 6 – 2x

2. Find points for each line

For y = x:

If x = 0, y = 0

⇒ (0, 0)

If x = 3, y = 3

⇒ (3, 3)

For y = 6 – 2x:

If x = 0, y = 6

⇒ (0, 6)

If x = 3, y = 0

⇒ (3, 0)

3. Graphical representation

Plotting these lines on a coordinate plane shows where they intersect.

4. Observe the intersection

The two lines intersect at the point (2, 2). At this point, both equations are satisfied:

2 – 2 = 0   ...(Correct)

2(2) + 2 = 4 + 2 = 6   ...(Correct)

The graphical solution to the system of equations is x = 2 and y = 2.