01 · STANDARD FORM
Linear Equation in Two Variables
An equation of the form ax + by + c = 0, where a, b, c are real numbers and a, b are not both zero (a² + b² ≠ 0), is called a linear equation in two variables x and y.
SOLVED EXAMPLE
Express 2x + 3y = 4.37 in the form ax + by + c = 0 and indicate values of a, b, c
Transpose 4.37 to the left side:
2x + 3y - 4.37 = 0
Comparing with ax + by + c = 0:
a = 2, b = 3, c = -4.37
Comparing with ax + by + c = 0:
a = 2, b = 3, c = -4.37
02 · SOLUTIONS
Infinitely Many Solutions
A linear equation in two variables has infinitely many solutions. Each solution (x, y) corresponds to a point on the line representing the equation.
FINDING SOLUTIONS
Find four different solutions for 2x + y = 7
1. Take x = 0: 2(0) + y = 7 ⟹ y = 7 ⟹ (0, 7)
2. Take x = 1: 2(1) + y = 7 ⟹ y = 5 ⟹ (1, 5)
3. Take x = 2: 2(2) + y = 7 ⟹ y = 3 ⟹ (2, 3)
4. Take y = 0: 2x + 0 = 7 ⟹ x = 3.5 ⟹ (3.5, 0)