Different systems of linear equations

An equation for a line can be called as a linear equation. The various forms of linear equation can look like:

• X = 4.6 – 5.2Y
• X = 7(5-Y)
• X + 3.2Y = 5.3
• X + 3.3Y – 5.3 = 0

And many more ways. 

To understand linear equations better, one can focus on this simple example. Imagine you went to a café and your sister asked their price for a cup of coffee and a cup of tea. Now, since you are unable to recall the price of coffee and tea, you say that the last time you placed an order for 2 cups of coffee and 1 cup of tea then the total price was 35Rs. On the other hand, today when you once again went to the shop and ordered 3 coffees and 2 teas the price was 55Rs. In these situations, linear equations can be used for getting to know the exact price of tea and coffee. 

System of Linear Equations

When two or more than two linear equations are together working with the same variables then it can be explained as a system of linear equations. 

For example – 

2Y + X = 5

-Y + X = 2

Important Points

• In a linear equation, solely simple variables can be there. That is x2, i2 cannot be there in linear equations. 
• An equation 2Y + X – I = 4 can be a form of linear equation.
• On the other hand, 2Y + X2 – I = 4 is not a form of linear equation. 
• A linear equation can be there in four dimensions, three dimensions, two dimensions, and many more. 
• There can be different ways of finding a solution for the linear equations. These ways include can be a graphical method, cross multiplication method, determinant method, substitution method, and elimination method. 

Linear Equations in two variables

A system of equations with an exclusive answer, infinitely several answers, or no answers can be called a linear equation in two variables. There might be an ‘n’ number of variables present in a system of linear equations. 

A linear equation in two variables can be explained as those algebraic equations which can be in the form z = ny + c wherein n can be the slope, c can be the z-intercept. 

Conclusion

As observed from the above section, the understanding of linear equations, the methods for solving them, and the examples for different linear equations have been now clearly understood. As understood from above, a linear equation can be defined as an equation for a line. For example, 

• X = 4.6 – 5.2Y
• When two or more than two linear equations are together working with the same variables then it can be explained as a system of linear equations. Apart from this, there can be several ways for finding a solution for the linear equations. These ways include can be a graphical method, cross multiplication method, determinant method, substitution method, and elimination method. 

Thus, it can be concluded that with the above section the various aspects of the linear equation have been clearly understood.