Solving equations means finding out the values of the variables, so that, it satisfies the given equation. We can solve the equations algebraically and graphically. The number of solutions in an equation depends upon the degree of the equation.
- If the degree of the equation is 1, then the equation will have one solution.
- If the degree of the equation is 2, then the equation will have 2 roots.
- If the degree of the equation is n, then the equation will have n roots.
Examples on Solving Equations:
Let us discuss solving equations with some of the examples.
Solve the equation 2x + 3 = 7.
The given equation is 2x + 3 = 7.
The equation has the degree as 1. So, the equation will have only one root.
2x + 3 = 7
In this, take 3 to right hand side. Then, we will get
2x = 7 - 3
2x = 4
Dividing both the sides by 2, we will get
x = 2.
The required solution for the given equation is 2.
Solve the given equation x2 - 1 = 0.
The given equation is x2 - 1 = 0.
We can write the given equation as (x) 2 - (1) 2 = 0.
This is in the form of (a)2 - (b)2, which is equal to (a + b) (a - b), where 'a' is equals to x and 'b' is equal to 1.
So now, we can write the given equation as (x - 1) (x + 1) = 0.
Now, make these two factors as equal to 0. Then, we will get it as
(x - 1) = 0 or (x + 1) = 0.
Now, x = 1 or x = -1.
The roots of the given equation are -1 and 1.
Solve the equation x2 - 3x + 2 = 0.
The given equation is x2 - 3x + 2 = 0.
The degree of the equation is 2. Then, we will get the number of solutions of the given equation as 2.
Now, let us solve the given equation by factorization method.
x2 - x - 2x + 2 = 0.
In the first two terms, take x as common and in second two terms, take - 2 as common term. Then,
x (x - 1) - 2 (x - 1) = 0
Again take (x - 1) as common. Then, we will get
(x - 1) (x - 2) = 0
If we equate this to zero, then we will get it as (x - 1) = 0 or (x - 2) = 0
Then, we will get the x values as 1 or 2.
The solutions of the equation are 1 and 2.