A Basic Introduction to System of Equations

system of equations

A system of Equations is a system of two or more equations, where we need to find the values of the unknown. To know the basics, students start with 2 linear equations to find the solution to a mathematical problem. To start with, we use two variables, x and y, and a constant value.

As we move on in mathematics, the system of equations gets tougher with many sets of equations to work with. The variables also tend to increase from x and y to z and so on. Sometimes, quadratic equations are also used within the set to find out the values of x, y, and z which may represent as coordinates over a three-dimensional axis. Eventually, if the equations get difficult over time, the main fundamental motive remains the same i.e. the point of intersection. Thus, the common solution to a set of linear equations is the point of intersection where both the lines meet.

Different solutions to problems

According to mathematics, there are times when two lines would not intersect at a single point. For instance, a parallel line never intersects and thus it has no solution. Sometimes some equations tend to look complicated, but after reducing them, they turn up to be the same equation. Thus there tends to be an infinite number of solutions.

Finding a solution using the graphing method

The graphing method is the easiest and most effective way to find the intersection of the system of equations. We can solve the equations by putting them on the same coordinate axis or plane. For examples of Graphing Methods, please visit Cuemath for different sets of problems.

Finding out a solution using the substitution method

There are times when the graphing method does not seem to be very effective to find the results. Thus, we use many algebraic methods to solve the equation with a set of unknown variables. 

One of the most interesting methods to find a solution to the equation is the substitution method. With the help of this method, we can easily get the value of a variable by inserting the value of an unknown into a different equation. This would help you come up with an equation using a single variable, with which we can find the value of the other variable as well. As we find out the value of one unknown, it becomes easier to find the value of the other by putting it in the equation.

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Finding out a solution using the elimination method 

The substitution method may not always be the best way to solve a problem. So, for this, we utilize the last method that is the elimination method.

The main objective of this method is to add 2 different equations to get rid of the variable. Sometimes for doing this, we need to multiply the equations with a number to eliminate a variable found in both the equations. At that point, when we have multiplied the equation and added it with the other, one unknown variable gets eliminated and we are left with the value of the other variable. Thus as we get the value of one unknown variable, we can insert the value within the equation and find out the value of the other variable easily. Thus, it becomes easier to find the solution to the equation.

So, to solve a system of equations, we need to use one of the three processes depicted above in this article. Cuemath helps you in finding out the solutions with their online math classes and different lessons available on their website.


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