A free online quadratic simultaneous equation solver that solve any system of equations, Shows all the workings step by step. Before we dive into how the online solver works, let’s get some basic on what qualifies as quadratic simultaneous equation. In particular, we will consider a system of quadratic and linear equation

A linear equation is an equation of the form y=ax+b, with the power of the variable x been one. On the other hand a quadratic equation is an equation of the form ax^2+bx+c where a\neq 0 . A combination of a linear and a quadratic forms a perfect system of equations or a pair of simultaneous equation. It is possible to solve such a system through the substitution method.

### Examples of Quadratic simultaneous equation

- 3x^2+4x-2=0,x+y=9
- x^2+x=2,x-y=7
- 2x^2+3x-12=0,x+3y=4
- 6x^2+4x=12,x+2y=6
- x^2+x=0,3x+y=2
- x^2+8y=13;2y+x=2
- (x^2)+(y^2)=1,y=2x-5

### A Free Quadratic simultaneous equation solver with steps

When solving a system of linear and quadratic equations using an online solver, you need more than just the answers. Our online calculator gives you a step by step solution for your system of equation. The calculator can be used to solve any systems of equations whether linear, quadratic or a combination of both. In addition, the system of equations calculator helps you find solution for linear or quadratic system of equations quickly and accurately. In addition, the calculator allows you to use any number of variables and up to 5 equations.

A better way to present solution for a system of equations is through the use of graphs. EquationCalc’s solver for simultaneous equations also has a graphing tool for representing graphical solution for simultaneous equations.

When solving a system of a linear and quadratic equations, there are usually 2 pairs of answers. Basically, quadratics represents conic section curves such as circle, parabola, ellipse and hyperbola. On the other hand, a linear equation represents a line on a plane. Therefore, a solution to the system would be the points where the graphs of the 2 equations intersect.
Quadratic simultaneous equation solver with steps

Solving simultaneous equations online using EquationCalc’s online Algebra calculator is fast and accurate. Furthermore, the calculator shows you all the workings and explanations on how to obtain the solutions.
Simultaneous equations substitution method calculator

Solving a system of equations consisting of a linear and a quadratic equation using the substitution method. It is easier to demonstrate how to go about solving such a system using an example.

### Example 1: Quadratic simultaneous equation

- y=x+2
- y=x^2+3x

**Step 1:**
Substitute the value of y in equation 2, the result is a linear equation with x as the only variable.

i.e.

2x+2=x^2+x
\Rightarrow x^2-x-2=0 (rearranging the terms)

The resultant quadratic equation can be solved using either the quadratic formula method or through factorization.

Let’s solve by factorization

x^2+x-2x-2=0

x(x+1)-2(x+1)=0

(x-2)(x+1)=0

\Rightarrow x-2=0 Or x+1=0 \Rightarrow1 x=2, Or x=-1

With the above pairs of solution, you can find the value or y by substituting the value of x in equation 1.

Thus y=(2)+2=4 (substituting x=2)
Or y = (-1)+2=1 (substituting x=-1)

Thus the solution for the above system of equation is:

(2,4) Or (-1,1)

Graphically, the solution represents points of intersection between the line y=x+2 and the conic section x^2+x-2x-2=0

View more Go to Solved Algebra examples with Steps

You may also use our system of equations solver for linear: systems of equations Solver

## Simultaneous linear equations solver that works

A free online system of equation solver, works with linear, non-linear equations of up to 5 variables. This online algebra calculator helps you find the solution for any system of equations. It works for any systems of equations. The calculator is free and comes with premium package for those that need more than just a solution. The premium package, gives you access to step by step solution including explanation on how an answer was arrived at. Solve for x and y simultaneously online using EquationCalc’s Online calculators.

## Simultaneous linear equations in two variables calculator

To solve a system of linear equations with 2 variables, you require at least 2 equations. Similarly, to solve a system with three variables requires you to have at least 3 equations. Thus, you can’t solve a system of equations if the number of variables is greater than the number of equations. Such systems have no solutions. Furthermore, a system of equation can also lack a solution, if the graphs of the resulting equations do not intersect at any given point

## Simultaneous equation solver with working

EquationCalc’s Algebra calculator for system of equations is like no other online calculators. The calculator shows you all the workings through a step by step solution strategy. It is an online solver for systems of equations. It shows all the workings including a step by step solution.

### How to use EquationsCalc’s Online Simultaneous equations Solver

How it Works

Here is a Worked example to illustrate how the simultanous calculator Works:

Using the calculator is quite easy and straightforward.

The following steps illustrate how to find solutions for quadratic simultaneous equations online.

**Step 1:** Enter your pairs or equations separated by a comma (,) or a semi-colon (;). (Note if you don’t you a separator, the calculator will output an error.

**Step 2:** Once you have ensured the input is correct, hit the Calculate Now button to obtain an instant solutions.

**Step 3:** Use the solution: Once you have received a solution, you can apply it as you may wish to solve your assignments or any given math problems. You can copy or print the solution for latter use.

## Learn how to solve quadratic simultanous equations algebraically with Examples

Perhaps it is best if you learnt math through examples. Checkout our algebra examples, each with a step by step solution. The Examples will also guide you on how to use this equation calculator to solve your algebra problems.

Go to Solved Quadratic Simultanous equations examples with Steps

**Acceptable Math symbols and their usage**

If you choose to write your mathematical statements, here is a list of acceptable math symbols and operators.

- + Used for Addition
- -Used for Subtraction
- *multiplication operator symbol
- /Division operator
- ^Used for exponent or to Raise to Power
- sqrtSquare root operator

Pi : Represents the mathematical Constant pi or

\pi
### What’s more or what are the limitations of the online algebra calculator

We love to hear your feedback. If you encounter any problems while using this calculator, please let us know:
Want to see more features? Send us your recommendations and app ideas. We are always working hard to make algebra easy and fun.