Linear equations are the equations with degree one variables. As linear algebra is the mathematics of data, the tools of linear algebra are used in many domains. In math, linear equations use two or more variables that produce a graph that proceeds in straight line, such as y = x + 2. A solution to the system of equations, the values of the point must be a solution for both equations. A printer prints 5 pages less in the second minute to what it prints in the first minute. If he prints 77 pages in two minutes, how many pages does he print in the first minute? when we come across such problems, we use linear equations to frame such statements into algebraic equations and get the answer!
Learning how to use and solve linear equations can be vital to entering some popular careers. Class 6 students can practice below problems and clear their concepts on linear equations.
Linear Equations Notes for Class 6
1. An equation made up of 2 algebraic expressions set equal to each other is called linear equation.
2. Standard form of linear equation
with one variable: ax + b = 0
with two variables: ax + by + c = 0
with three variables: ax + by + cz + d = 0
3. Graph of linear equations is always a straight line.
4. A linear equation in two variables : contains two variables, where value of both the variables depend on each other.
5. Slope Intercept Form, Two Point slope form are special forms of linear equations with two variables.
Example Problems for Class 6
Below we have listed some of the examples for the class 6 students based on their latest syllabus. Practice below problems and get exam ready.
Example 1: Solve 12(m + 2) = 1/2(4m - 12) - 14
Solution: 12(m + 2) = 1/2(4m - 12) - 14
Using distributive property
12m + 24 = 2m - 6 - 14
12m + 24 = 2m - 20
12m - 2m = -20 - 24
10m = -44
m = -44/10
The value of m is -44/10
Example 2: A rectangle has width which is thrice its length . The perimeter of the rectangle is 80 m. Find the length of the rectangle?
Solution: The perimeter of the rectangle whose length and breadth are x and y respectively.
Perimeter of the rectangle formula = 2(x + y) units
Perimeter of rectangle = 80 (given)
2(x + y) = 80
y = 3x (according to statement)
2(x + 3x) = 80
2(4x) = 80
8x = 80
or x = 10
Therefore the length of the rectangle is 10 m.
Example 3: Radhika travels at speed of x m/s for one minute, still she finds herself 49 m away from a point. If the destination is 87 m away from that point. Find the distance between the starting point and the destination?
Distance travelled by Radhika in 1 minute = (x) × (60) that is 60x
Distance between the starting point and the destination is
= 60x + 49 + 87
= (60x + 136) m
Since we do not know the value of x. This is the answer.
Practice Problems For Class 6
Problem 1: Find the two digit number such that it is an even number and when divided by 3 leaves remainder of 2 and lies between 80 and 90.
Problem 2: The sum of two numbers is 100. One of the numbers lesser than the other by 5. Find the numbers.
Problem 3: Sujatha is 7 years older than Parth. four years later, Sujatha will be twice as old as Parth. Find their present ages.