System of Linear Equations

The topic of linear equations in mathematics has contributed a very large and important role to do any mathematics without the knowledge of the basic linear equations and how to find the solutions of that equation. The linear equation is said to be having the highest variable power of one, and if a graph is drawn for the same equation, it will always make a straight line. There are multiple ways to find the solution of any given equation, this helps you find what fits in with the values present in the equation. The equation can also be in 2 variables or 3 variables and can even be with multiple variables more than 3. Follow the article for more important information about the linear equations.

Linear Equations

A linear equation can be easily recognized as an equation where the highest degree of the variable of the equation is one. This can also be referred to as a one-degree equation, if the graph has been called according to the linear equation, it will always be a straight line.

Considering a standard form of a linear equation that is in one variable Ax+B=0: here, the A is the coefficient of the variable X and B can be taken as the constant in the linear equation. But if we talk about the linear equation in two variables then the new equation looks like Ax+By=C; in this equation too A and B are the two coefficients of the two variables X and Y and C is the constant in the equation.

There are several methods to solve a particular linear equation such as the graphical method, the substitution method, the elimination method, the cross-multiplication method, or by using the determinant method. 

Things to keep in mind: There will be no change in the linear equation if the same number has been added or subtracted from the equation from both sides of the equation. The values of the variables after applying various methods are known as the roots of that particular equation. In both the cases of linear equations whether in one variable or two variables if a graph has been drawn it will always form a straight line.

The linear equation is a type of equation in which the highest degree of the respective variable is 1, always. This is called a one-degree equation; some examples of linear equations are m+2=0; x+y=9; 7x-9=10.

There can be three forms of any type of linear equation which are the slope-intercept form, the point-slope form, and the standard form.

In the slope-intercept form of the linear equation the equation is presented as y=mx+c;

Here, x and y are the coordinates of the point, the slope of the given line, and c is the constant.

(Slope: the ratio of the change in the y coordinate to the change in the x coordinate is referred to as its slope.)

m= (y2-y1)/(x2-x1)

The slope of any line can also be referred to as the gradient of the line.

In the points of form a linear equation the straight line of the equation is considered to be in the XY plane so that:

y-y1 = m(x-x1)

Here, the (x1,y1) are the main coordinates of any point.

The standard form has a combination of constants and the different variables, such as:

Ax+B=0; Ax+By+C=0 and when we talk about three variable representations then the equation is in the form of ax+by+cz+d=0.

Conclusion

As has been mentioned above, linear equations are a very basic and important part of mathematics, it is difficult to solve any equation without knowing it. In the above article, the same has been given. Linear equations are the type of equation having the highest variable power of one. It is of three forms the point-slope form, the standard form, and the slope-intercept form.