A System of Linear Equations is a pair of linear equations having a unique solution. To understand the system of linear equations let’s take an example related to our daily life. 

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The total cost of 2 kg sugar and 1 kg tea is Rs. 180 while the total cost of 1 kg sugar and 2 kg tea is Rs. 240. Find the rate of each per kg.


Here, we need to find the cost of 1 kg sugar as well as the cost of 1 kg tea.


Let the cost of 1 kg sugar be Rs. x
and cost of 1 kg tea be Rs. y


The cost of 2 kg sugar and 1 kg tea = Rs. 180
Therefore, 2x + y = 180 …………….(i)


Also, the cost of 1 kg sugar and 2 kg tea = Rs. 240
Therefore, x + 2y = 240 …………….(ii)


Here, x and y are two variables in each of a pair of above linear equations. If we show them in a graph, each equation gives a straight line and they intersect with each other at a unique point which gives the values of x and y satisfying both the equations. Such a pair of linear equations which satisfied by a unique solution is called a system of linear equations.


There are 3 different methods for solving a system of linear equations:

• Substitution Method
• Elimination Method
• Graphical Method

Do you have any questions regarding the System of Linear Equations? You can ask here in the comment section below.

A linear equation represents a straight line on a graph. If two linear equations whose straight lines intersect each other at a point, they are called system of linear equations. The point of intersection is the common solution to those linear equations, and hence is the solution of system of linear equations.

Among the various methods to solve simultaneous equations, the Elimination Method is one of the most popular and easiest methods to solve the pair of simultaneous equations in two variables x and y.

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In this method, one variable either x or y is eliminated to find the value of another variable. And, for that, we need to make coefficients of any one variable equal by multiplying or dividing the equations by the least number so that the coefficients of x or y become equal in both the new equations. 

Then, by adding or subtracting according to these equal coefficients have opposite or same sign respectively, we get an equation which will have only one variable. Then, simplification will give the value of that variable.

 

After solving the value of either x or y obtained from the above steps is substituted in any one of the given equations to get the value of the other variable.

What is the Substitution Method in Math?

 

The method of solving simultaneous equations by putting the value of one variable in terms of another variable from one equation to another equation is called the Substitution Method in Math.

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10 Math Problems officially announces the release of Quick Math Solver and 10 Math Problems, Apps on Google Play Store for students around the world.

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What are Simultaneous Equations? What is mean by Solving Simultaneous Equations?

 

Simultaneous Equations are a pair of equations having a unique solution that satisfies both equations. And, Solving Simultaneous Equations means finding that unique solution.

 

For example: x + y = 5 and x – y = 3 are a pair of simultaneous linear equations. And, x = 4, y = 1 are the unique solutions that satisfy both the equations.

Read Simultaneous Linear Equations for more details.

What is a linear equation?

 

The definition of linear equation is: “The first degree equations in one, two, or three variables are called Linear Equations.”

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10 Math Problems officially announces the release of Quick Math Solver and 10 Math Problems, Apps on Google Play Store for students around the world.

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So, the equations of the form: ax + b = 0, ax + by + c = 0 and ax + by + cz + d = 0 are linear equations in one, two and three variables x, y and z where a, b, c and d are real numbers and not equal to zero at a time.

 

x = 1, 2x + 3 = 0, x + 4y = 7, 5x – 2y = 3, x + 3y – 4z = 1 etc. are some examples of linear equations.