System of equations online solver

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Suppose we have system of two equations with two unknowns:

x25y245y3x3

Rewrite the equations in canonical way:

x245y241y3x535

The first equation of the system is an ellipse with a semi-major axis equal to 2 and a semi-minor axis equal to 25 . The second equation is the straight line with tangent equal to 35 and the value of the segment to be cut off on Oy axis equal to 35 .

Let's draw the above on a schematic diagram:

schematic diagram of the system of equations

The intersection points of straight line with ellipse M1(x1,y1) and M2(x2,y2) are solutions of the initial system of equations. Since the line intersects the ellipse only in two point indicated above, there are no other solutions.

Just now we have considered so-called graphical method of solving system of equations, which is well suited for solving a system of two equations with two unknowns. As the number of equations increase, the solutions will be points in multidimensional space and it will significantly complicate the task.

If in order to solve the initial system of equations we'll use more universal substitution method, we'll get the following result:

x19235140.452122y135235700.871273x29235141.73784y235235700.442702

Our online calculator, based on Wolfram Alpha system is able to solve many different types of systems of equations.

System of equations calculator
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Given:x25y245y3x3Find:x= ?y= ?
System of linear algebraic equations you want to solve:


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