Introduction to linear equations in math:
A linear equations is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable. Linear equations can have one or more variables. Linear equations occur with great regularity in mathematics. The general form of the liner equation is y =mx +b. Otherwise it can be written as ax + by=c. Here we are going to how to solve the liner equation in math and its example problems. (Source from Wikipedia)
Solving method for linear equations in math:
Elimination method
Substitution method
Example problems for solving linear equations in math:
Example: 1
Solve the following liner equation using elimination method 2x+3y = 5 and x + y = 2
Solution:
2x+3y = 5 -----------------------1
x + y = 2 -------------------------2
Multiply equation(2) by 2, we get
2x + 2y = 4 ----------------------3
Take equation 1 and 3 subtract equation 3 from 1 we get
2x+3y = 5
2x + 2y = 4 (change the sign and add)
--------------------
y = 1
----------------
Now we have to find the x value
Substitute y value in to the equation 1 we get
2x + 3y = 5
2x + 3 (1) = 5
2x + 3 = 5
Add both sides -3 we get
2x + 3 - 3 = 5 - 3
2x = 2
Divide both sides 2 we get
x = 1
Therefore the solution of the given liner equation is x = 1 and y = 1
Example: 2
Solve the following liner equation using substitution method
x+4y = 10
x+12y = 20
Solution:
x+4y = 10 ----------------------- 1
x+12y = 20 ----------------------2
Form equation 1 we can write
x = 10 - 4y -----------------------3
Substitute the x value into the equation 2
10-4y+12y = 20
10 + 8y = 20
Add both sides -10
8y = 20-10
8y = 10
y = `10 / 8`
y = `5/4`
Substitute y value into equation 3 we get
x = 10 – 4`(5/4)`
x = 10 -`20/4`
x = `(40 - 20) / 4`
x = `20/4`
x = 5
Therefore the solution of the given liner equation is x = 5 and y =` 5/4`
A linear equations is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable. Linear equations can have one or more variables. Linear equations occur with great regularity in mathematics. The general form of the liner equation is y =mx +b. Otherwise it can be written as ax + by=c. Here we are going to how to solve the liner equation in math and its example problems. (Source from Wikipedia)
Solving method for linear equations in math:
Elimination method
Substitution method
Example problems for solving linear equations in math:
Example: 1
Solve the following liner equation using elimination method 2x+3y = 5 and x + y = 2
Solution:
2x+3y = 5 -----------------------1
x + y = 2 -------------------------2
Multiply equation(2) by 2, we get
2x + 2y = 4 ----------------------3
Take equation 1 and 3 subtract equation 3 from 1 we get
2x+3y = 5
2x + 2y = 4 (change the sign and add)
--------------------
y = 1
----------------
Now we have to find the x value
Substitute y value in to the equation 1 we get
2x + 3y = 5
2x + 3 (1) = 5
2x + 3 = 5
Add both sides -3 we get
2x + 3 - 3 = 5 - 3
2x = 2
Divide both sides 2 we get
x = 1
Therefore the solution of the given liner equation is x = 1 and y = 1
Example: 2
Solve the following liner equation using substitution method
x+4y = 10
x+12y = 20
Solution:
x+4y = 10 ----------------------- 1
x+12y = 20 ----------------------2
Form equation 1 we can write
x = 10 - 4y -----------------------3
Substitute the x value into the equation 2
10-4y+12y = 20
10 + 8y = 20
Add both sides -10
8y = 20-10
8y = 10
y = `10 / 8`
y = `5/4`
Substitute y value into equation 3 we get
x = 10 – 4`(5/4)`
x = 10 -`20/4`
x = `(40 - 20) / 4`
x = `20/4`
x = 5
Therefore the solution of the given liner equation is x = 5 and y =` 5/4`
