System of Equations Solver


Instructions: This System of Equations Solver allows you to find the intersection point (if any) between two straight lines. You need to provide the equation of each line. The solver will compute the intersection point and it will make a graph. For example in the first box you can type "2x + 1", and in the second box you can type "x-1"


Equation of the first line: \(y_1\) =


Equation of the second line: \(y_2\) =



System of Equations Calculator

Solving systems of equation is a common task in Algebra, because of its multiple applications. Either when you are solving a simple word problem or a complex allocation system, you are likely to end up solving a system of equations.

There are many types of systems, with different characteristics and specific features. Most systems will com defined with specific numbers whereas others come with literal constants, and are called literal equations.

The good thing about a system of equations is that there are some standard ways of solving them. Indeed, based on the coefficients in the system, we are able to tell whether the system has a unique solution, or whether the system has many (infinite) solutions, or whether the system does not have solutions.

Solving System of Equations Graphically

This approach only works for systems with two equations and two variables. The way to go is to graph each equation as a function of one of the variables (typically, the variables are \(x\) and \(y\), and customarily \(y\) is used as the dependent variable). The resulting graphs will be two lines.

By looking at the graph, we see that if the lines intersect, then there is a unique solution. Then, if the lines are parallel, we conclude that there are no solutions. And the lines overlap (so they are the same line), then we have infinite solutions.

Solving System of Equations by substitution

Another way of solving systems of equations is to write one variable in terms of the others and replace in the other equations. This works fairly well on 2x2 systems of equations, but it can get cumbersome for larger systems

Solving System of Equations by substitution

Another way of solving systems of equations is to write one variable in terms of the others and replace in the other equations. This works fairly well on 2x2 systems of equations, but it can get cumbersome for larger systems

A good System of equations Calculator

You can Use this solver if you want to solve a 2x2 system of linear equations. The approach used by this calculator is the use of Cramer's rule to solve a 2x2 system of equations. The good thing about Cramer's method is that it works fine for small or larger systems, the approach is the same

For larger systems of equations, the best alternative is to use the Gaussian elimination method, which systematically deals with linear systems of any size.




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