Question

Draw the graph of the following equations and find their point of intersection.

x – 2y = 0 and 2x + 3y = 7

Answer 1

1. Solve for y in both equations

To graph the lines, it is easiest to express them in slope-intercept form (y = mx + c):

Equation 1: x – 2y = 0

⇒ 2y = x

⇒ `y = 1/2 x`

Equation 2: 2x + 3y = 7

⇒ 3y = 7 – 2x

⇒ `y = (7 - 2x)/3`

2. Determine points for plotting

We can find two points for each line to draw them accurately:

For x – 2y = 0:

If x = 0, y = 0.

Point: (0, 0)

If x = 4, y = 2.

Point (4, 2).

For 2x + 3y = 7:

If x = 2, `y = (7 - 2(2))/3` = 1.

Point: (2, 1).

If x = 3.5, `y = (7 - 2(3.5))/3` = 0.

Point: (3.5, 0).

3. Calculate the intersection point

To find the intersection algebraically, substitute x = 2y (From equation 1) into equation 2:

2(2y) + 3y = 7

4y + 3y = 7

7y = 7

⇒ y = 1

Substituting y = 1 back into x = 2y:

x = 2(1)

x = 2

The two lines intersect at the point (2, 1).