Question

Solve the following system of equations graphically:

2x + 3y – 4 = 0, 3x – y + 5 = 0

Answer 1

1. Find coordinates for line 1: 2x + 3y – 4 = 0

Express y in terms of x:

3y = 4 – 2x ⇒ `y = (4 - 2x)/3`

Choose simple values for x to calculate corresponding integer values for y:

If x = –1, then y = `(4 - 2(-1))/3 = 6/3 = 2` → Point: (–1, 2)

If x = 2, then y = `(4 - 2(2))/3 = 0/3 = 0` → Point: (2, 0)

If x = 5, then y = `(4 - 2(5))/3 = (-6)/3 = -2` → Point: (5, –2)

2. Find coordinates for line 2: 3x – y + 5 = 0

Express y in terms of x:

y = 3x + 5

Choose values for x to calculate corresponding values for y:

If x = –1, then y = 3(–1) + 5 = 2 → Point: (–1, 2)

If x = 0, then y = 3(0) + 5 = 5 → Point: (0, 5)

If x = –2, then y = 3(–2) + 5 = –1 → Point: (–2, –1)

Graphical Representation

Plotting these coordinates on a Cartesian plane reveals the intersection point:

As shown in the graph, both straight lines intersect exactly at the coordinates (–1, 2).

Therefore, the solution is x = –1 and y = 2.