Linear equation is that field of algebra where each term is either a constant or a product of constant with the first power of a variable.
The term 'linear' defines that such equations ( y = mx + c) represent straight lines in Cartisian Coordinates.
In 'general' form of representation of linear equations, all the variables and constants are kept at Left Hand Side (LHS) and equated to zero (RHS).
In 'standard' form, the variables formulate the LHS and the constant term(s) is at RHS.
Example: General form: 3x + 4y - 10 + a = 0.
Standard form: 3x + 4y = 10 - a.
Linear Equation Variables do not have: oexponents (or powers) For example, x square or x 2 omultiplied or divided values of each other For example:"x" times "y" or xy; "x" divided by "y" or x/y oa root sign or square root sign (sqrt) For example:"square root of x"; sqrt (x) Consider a problem: I had Rs.
100 and I spent Rs.
75, calculate the amount of money left with me.
Solution: Let the amount of money left with me be x.
75 + x =100 => x=25.
Problem 2: Example: There are two numbers.
One number is 3 less than another number.
If the sum of the two numbers is 27, find each number.
Solution:Given- first number = x, second number = x-3, sum = 27.
Find- both the numbers.
Sum = 27 x + (x - 3) = 27.
2x - 3 = 27 2x = 27 + 3 = 30.
x = 30/2 = 15.
SOLUTION - one number is 15 and the other is (15 - 3), that is 12.
Putting 15 as x in Step 2.
LHS: 15 + (15 -3) = 15 + 12 = 27 =RHS.
Hence, our answer is correct.