0In mathematics there are two types of quantities namely constants and variables.
- Constants are those quantities whose value will not change.
- Variables are those quantities whose values will change with respect to time and place.
There are 4 fundamental operations in mathematics namely addition, subtraction, multiplication and division
When the constants and variables are connected with all or some of these operations we get mathematical expressions.
When mathematical expressions are connected by equality sign then it is called an equation.
Constants are generally denoted by a, b, c, d, e,......
Variables are generally denoted by x, y, z, p, q,..........
Linear equation in one variable:-
I purchased 10 pens at 35 rupees each and I got 650 rupees back when I gave a 1000. RS note
This can be put in the form of an equation as follows
35X10 +650 =1000
35x+650 =1000 then what is the value of X?
Solution:
35x=1000-650
35x=350
x=350/35
x=10
Equations in 2 variables is called a bivariate equation.
To solve for two variables we should have two equations in two variables
eg.
2x+3y=10................(1)
3x+2y=20.................(2)
eq. (1)x3 gives 6x+9y=30...........(3)
eq.(2)x2 gives 6x+4y=40............(4)
eq.(3)-eq.(4)m gives 5y=-10
y=-10/5=-2
sub. y=-2 in eq. (1) it gives
2x+3*(-2)=10
2x-6=10
2x=10+6
2x=16
x=16/2
x=8
hence the solution is
x=8 and y=-2
