Hello,
I think you have to know the linear equation, quadratic equation, and cubic equation. Some of them have one variable, two variables or three variables. We need some method to know the value of these variables.
Various methods we use to find the value of the variable such as the Cross multiplication method, Substitution method, Elimination method, Factorisation method, etc.
In this article we are going to learn the cross multiplication method and how to solve linear equation in two variable to find the solution.
The following points on the cross multiply method we will cover:
- What is linear equation in two variables?
- What is cross multiplication method?
- How to do cross multiplication?
- Cross multiplication method formula.
- Cross Multiplication Method questions and answers.
Ok So, now we start our first topic and learn the linear equation.
What is Linear Equation in two variables?
An equation has two variables and the higher degree is one is known as linear equation in two variables.
And when we talk about two linear equations with two variables then it is known as pair of linear equations in two variables.
What is Cross Multiplication Method?
The cross multiplication method is a method to find the solutions or values of any variable in a linear equation.
Other than cross multiply we use the substitution method and the elimination method.
But first, we learn how to do cross multiply to find x.
How to do cross multiplication?
As its name says we do cross multiply in the fractions which lies in Right Hand Side and in Left Hand Side.
Let's take some examples for better understanding and learn how to cross multiply.
Example: Find the value of x if (2x/2) = (3/5).
Solution:
⇒ (2x/2) = (3/5)
⇒ 2x*5 = 3*2
⇒ 10x = 6
⇒ x = 6/10
⇒ x = 3/5
Example: If (3x+5)/2 = (5+x)/3 then what is the value of x?
Solution:
⇒ (3x+5)/2 = (5+x)/3
⇒ 3*(3x+5) = 2*(5+x)
⇒ 9x+15 = 10+2x
⇒ 9x-2x = 10-15
⇒ 7x = -5
⇒ x = -5/7
I think now we have a better understanding of how to do cross multiply. Let's learn the cross multiply formula.
Cross Multiplication Method Formula
In the cross-multiplication method, we use coefficients of variables of a linear equation. The general form of a pair of linear equations in two variables is -
a₁x+b₁y+c₁=0
a₂x+b₂y+c₂=0
Where,
- a₁ & a₂ are the coefficients of x
- b₁ & b₂ are the coefficients of y
- c₁ & c₂ are constant terms.
The formula for Cross-multiplication method:-
⇒ x = y = 1
(b₁c₂)-(b₂c₁) (c₁a₂)-(c₂a₁) (a₁b₂)-(a₂b₁)
This formula we use in cross method Now it's time to learn how to solve linear equation in two variable by cross multiplication method.
How to solve linear equation in two variable?
To learn the cross multiplication steps let's take an example for better understanding.
Example: Solve the following pair of linear equations by cross-multiplication method.
2x+3y-46=0
3x+5y-74=0
Solution:
First, we will compare the given equations, by the general form of linear equation in two variables:
On comparing we get a₁=2, a₂=3, b₁=3, b₂=5, c₁=-46, and c₂=-74.
Now we will put all the above values in cross-multiplication formula to find the values of variables x & y.
⇒ x = y = 1
(b₁c₂)-(b₂c₁) (c₁a₂)-(c₂a₁) (a₁b₂)-(a₂b₁)
⇒ x = y = 1
(3*-74)-(5*-46) (-46*3)-(-74*2) (2*5)-(3*3)
⇒ x = y = 1
-222+230 -138+148 10-9
⇒ x = y = 1
8 10 1
Now we are equating variable terms and constant terms to find the value of the variable by cross multiply.
⇒ x/8 = 1/1 and ⇒ y/10 = 1/1
⇒ x*1 = 1*8 and ⇒ y*1 = 1*10
⇒ x = 8 and ⇒ y = 10
FAQ's on Linear equations in two variables
What means the equation in two variables?
Any expression that has an equal sign is known as an equation and an equation that has two variables is known as two-variable equation.
Example:
One variable equations = 2x+5=1, 9y=4, 12-3z=1, etc.
Two variable equations = 3z+5y=0, 6x+5y-8=0, etc.
What is the general form of linear equation in two variables?
The general form of linear equation in two variables are:
a₁x+b₁y+c₁=0
a₂x+b₂y+c₂=0
What is Cross multiplication method formula?
⇒ x = y = 1
(b₁c₂)-(b₂c₁) (c₁a₂)-(c₂a₁) (a₁b₂)-(a₂b₁)
