Today our topic of discussion is Equations in One Variable.
Equations in One Variable
Equations in One Variable
We have known in the previous class what equation is and learnt its usage. We have also learnt the solution of simple equations with one variable and acquired knowledge thoroughly about the solution of simple equations by forming equations from real life problems.
In this chapter, linear and quadratic equations and identities have been discussed and their usages have been shown to solve the real life problems.
At the end of the chapter, the students will be able to-
→ explain the conception of variable.
→ explain the difference between equation and identity. solve the linear equations.
→ solve by forming linear equations based on real life problems.
→ solve the quadratic equations and find the solution sets.
→ form the quadratic equations based on real life problems and solve.
Variable
We know, x + 3 = 5 is an equation. To solve it, we find the value of the unknown quantity. Here the unknown quantity is a variable. Again, to solve the equation x + a = 5 we find the value of x, not the value of a. Here, r is assumed as variable and a as constant.
In this case, we shall get the values of or in terms of a. But if we determine the value of a, we shall write a = 5 – xz that is, the value of a will be obtained in terms of z. Here a is considered a variable and ra constant.
But if no direction is given, conventionally is considered a variable. Generally, the small letter a, y, z ! the ending part of English alphabet are taken as variables and a, b, c, the starting part of the alphabet are taken as constants.
The equation, which contains only one variable, is called a linear equation with one variable. Such as, x + 3 = 5 ,x² – 5x + b = 0 ,2y² + 5y – 3 = 0 etc.
If a set, S ={ x:x ∈ R,1≤ x ≤10} . may be any real number from 1 to 10. Here, is a variable. So, we can say that when a letter symbol means the element of a set, it is called variable.
Degree of an equation: The highest degree of a variable in any equation is called the degree of the equation. Degree of each of the equations x + 1 = 5, 2x – 1 = x + 5, y + 7 = 2y – 3 is 1; these are linear equations with one variable.
Again, the degree of each of the equations x² + 5x + 6 = 0 ,y² – y = 12 ,4x² – 2x = 3 – 6x is 2 i these are linear equations with two variable. The equation 2x³ – x² – 4x + 4 = 0 is the equation of degree 3 with one variable.
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