An algebraic expression with degree 1 is called as a linear expression. The standard form of a line is Ax + By = C. Here A, B and C are constants x and y are variables So Ax+ By = c is a linear equation with two variables.Linear Equations can be represented in many forms.
A linear equation may have any number of variables. Suppose it is n then the linear equation is of the form a1x1 + a2x2+a3x3+…………+an xn = CC
C is a constant and x1, x2…….,xnare variables
1)What is the degree of x² + 3y = 12 ?
The power of x is 2 and the power of y is 1.
Degree = Highest power = 2
Example 1: 2x + 3 = 19 (Linear equation in one variable)
2x +3- 3 = 19– 3 (Add -3 on both sides)
2x/2 = 16/2(Divide by 2 on both sides)
x = 8
Example 2: 4x + 3y + 7 = 0 (Linear equations in two variables x & y)
NOTE: Number of solutions of an equation is equal to the degree of the equation.
4) Choose a Linear expression from the following
(c) 2xy + 6
(d) 7x + 9y
5) x + 2² = 12. Solve for x
x + 4 = 12 (Square the number)
x + 4 – 4= 12–4 (Add -4 on both sides)
x = 8