Equations with linear expressions in one variable only are called
Answers
Answered by
6
What is an equation?.
An equation is a statement in which two algebraic expressions are equal. Linear Equations of one variable is the equation which involves only one variable. General form of a linear equation of one variable is ax + b = 0, where a is not equal to 0.
Let us discuss the situation that " A farmer traveled a distance of 61 km in 9 hrs. He traveled partly on foot at an average of 4 km / hr and partly on bicycle at an average speed of 9 km/hr. Find the distance traveled by him on foot ". If we look at this situation it seems to be complicated. But we can easily solve this types of situations framing linear equations of one variable.
Linear Equation: The general form of Linear Equations are ax + b = 0, where a is not equal to 0.
Solution of a Linear Equation: The value of the variable which when substituted for the variable in the equation, makes its two sides equal, is called a solution ( 0r root) of the equation.
Example 1 : Verify that x = 2 is a solution of the linear equation 2x + 7 = 13 - x
Solution: Substituting x = 2 in 2x + 7 = 13 - x, we get
2 ( 2) + 7 = 13 - 2
=> 4 + 7 = 11
=> 11 = 11
=> x=2 is the solution of the given equation.
Example 2: Verify that x = 3 is not a solution of the equation, 3x - 5 = 4 + x
Solution: Substituting x = 3, in 3x - 5 = 2 + x, we get,
3 (3) - 5 = 2 + 3
=> 9 - 5 = 5
=> 4 = 5, which is not true
Therefore, x = 3 is not a solution of the given equation.
How to solve Linear Equations in one variable:
Rules for solving linear equations:
The equality of a linear equation is not changed,
Rule 1 : When the same number is added to both sides of the equation.
Rule 2: When the same number is subtracted from both sides of the equation.
Rule 3 : When both sides of the equation are multiplied by the same non-zero numbers.
Rule 4: When both sides of the equation are divided by the same non-zero number.
An equation is a statement in which two algebraic expressions are equal. Linear Equations of one variable is the equation which involves only one variable. General form of a linear equation of one variable is ax + b = 0, where a is not equal to 0.
Let us discuss the situation that " A farmer traveled a distance of 61 km in 9 hrs. He traveled partly on foot at an average of 4 km / hr and partly on bicycle at an average speed of 9 km/hr. Find the distance traveled by him on foot ". If we look at this situation it seems to be complicated. But we can easily solve this types of situations framing linear equations of one variable.
Linear Equation: The general form of Linear Equations are ax + b = 0, where a is not equal to 0.
Solution of a Linear Equation: The value of the variable which when substituted for the variable in the equation, makes its two sides equal, is called a solution ( 0r root) of the equation.
Example 1 : Verify that x = 2 is a solution of the linear equation 2x + 7 = 13 - x
Solution: Substituting x = 2 in 2x + 7 = 13 - x, we get
2 ( 2) + 7 = 13 - 2
=> 4 + 7 = 11
=> 11 = 11
=> x=2 is the solution of the given equation.
Example 2: Verify that x = 3 is not a solution of the equation, 3x - 5 = 4 + x
Solution: Substituting x = 3, in 3x - 5 = 2 + x, we get,
3 (3) - 5 = 2 + 3
=> 9 - 5 = 5
=> 4 = 5, which is not true
Therefore, x = 3 is not a solution of the given equation.
How to solve Linear Equations in one variable:
Rules for solving linear equations:
The equality of a linear equation is not changed,
Rule 1 : When the same number is added to both sides of the equation.
Rule 2: When the same number is subtracted from both sides of the equation.
Rule 3 : When both sides of the equation are multiplied by the same non-zero numbers.
Rule 4: When both sides of the equation are divided by the same non-zero number.
Similar questions