Solve equations and systems with Step-by-Step Math Problem Solver (2025)

Equations

The equations section of QuickMath allows you to solve and plot virtually any equation or system of equations. In most cases, you can find exact solutions to your equations. Even when this is not possible, QuickMath may be able to give you approximate solutions to almost any level of accuracy you require. It also contains a number of special commands for dealing with quadratic equations.

Solve

The Solve command can be uses to solve either a single equation for a single unknown from the basic solve page or to simultaneously solve a system of many equations in many unknowns from the advanced solve page. The advanced command allows you to specify whether you want approximate numerical answers as well as exact ones, and how many digits of accuracy (up to 16) you require. It also allows you to eliminate certain variables from the equations.

Go to the Solve page

Plot

The Plot command, from the Graphs section, will plot any function of two variables.In order to plot a single function of x, go to the basic equation plotting page, where you can enter the equation and specify the upper and lower limits on x that you want the graph to be plotted for. The advanced plotting page allows you to plot up to 6 equations on the one graph, each with their own color. It also gives you control over such things as whether or not to show the axes, where the axes should be located, what the aspect ratio of the plot should be and what the range of the dependent variable should be. All equations can be given in the explicit y = f(x) form or the implicit g(x,y) = c form.

Go to the Equation Plotting page

Quadratics

The Quadratics page contains 13 separate commands for dealing with the most common questions concerningquadratics. It allows you to : factor a quadratic function (by two different methods); solve aquadratic equation by factoring the quadratic, using the quadratic formula or by completing the square;rewrite a quadratic function in a different form by completing the square; calculate the concavity,x-intercepts, y-intercept, axis of symmetry and vertex of a parabola; plot a parabola; calculate thediscriminant of a quadratic equation and use the discriminant to find the number of roots of a quadraticequation. Each command generates a complete and detailed custom-made explanation of all the steps needed tosolve the problem.

Go to the Quadratics page

By an equation we mean a mathematical sentence that states that two algebraicexpressions are equal. For example, a (b + c) =ab + ac, ab = ba, and x2-1= (x-1)(x+1) are all equations that we have been using. We recall that wedefined a variable as a letter that may be replaced by numbers out of a givenset, during a given discussion. This specified set of numbers is sometimescalled the replacement set. In this chapter we will deal with equationsinvolving variables where the replacement set, unless otherwise specified, isthe set of all real numbers for which all the expressions in the equation aredefined.

If an equation is true after the variable has been replaced by a specificnumber, then the number is called a solution of the equation and is said tosatisfy it. Obviously, every solution is a member of the replacement set. Thereal number 3 is a solution of the equation 2x-1 = x+2, since 2*3-1=3+2. while1 is a solution of the equation (x-1)(x+2) = 0. The set of all solutions of anequation is called the solution set of the equation.

In the first equation above {3} is the solution set, while in the secondexample {-2,1} is the solution set. We can verify by substitution that each ofthese numbers is a solution of its respective equation, and we will see laterthat these are the only solutions.

A conditional equation is an equation that is satisfied by some numbers fromits replacement set and not satisfied by others. An identity is an equation thatis satisfied by all numbers from its replacement set.

Example 1 Consider the equation 2x-1 = x+2

The replacement set here is the set of all real numbers. The equation isconditional since, for example, 1 is a member of the replacement set but not ofthe solution set.

Example 2 Consider the equation (x-1)(x+1) =x2-1

The replacement set is the set of all real numbers. From our laws of realnumbers if a is any real number, then (a-1)(a+1) = a2 -1

Therefore, every member of the replacement set is also a member of the solutionset. Consequently this equation is an identity.

Example 3 Consider
Solve equations and systems with Step-by-Step Math Problem Solver (1)

The replacement set for this equation is the set of real numbers except 0,since 1/x and (1- x)/x are not defined for x = 0. If a is any real number in the replacement set, then

Solve equations and systems with Step-by-Step Math Problem Solver (2)

so that the original equation is an identity.

Example 4 Consider
Solve equations and systems with Step-by-Step Math Problem Solver (3)

The replacement set is the set of all non-negative real numbers, sinceSolve equations and systems with Step-by-Step Math Problem Solver (4)is not a real number if x is negative. The equation is conditional since, for example, 4 is a member of the replacement set but not of the solutionset.

Solve equations and systems  with Step-by-Step Math Problem Solver (2025)

FAQs

Is there a website that solves math problems with steps for free? ›

Symbolab is the best step by step calculator for a wide range of math problems, from basic arithmetic to advanced calculus and linear algebra. It shows you the solution, graph, detailed steps and explanations for each problem.

How to solve a system of equations step by step? ›

To Solve a System of Equations by Elimination
  1. Write both equations in standard form. ...
  2. Make the coefficients of one variable opposites. ...
  3. Add the equations resulting from Step 2 to eliminate one variable.
  4. Solve for the remaining variable.
  5. Substitute the solution from Step 4 into one of the original equations.

Does Photomath solve systems of equations? ›

Photomath supports arithmetic, integers, fractions, decimal numbers, roots, algebraic expressions, linear equations/inequalities, quadratic equations/inequalities, absolute equations/inequalities, systems of equations, logarithms, trigonometry, exponential and logarithmic functions, derivatives and integrals.

How do you solve math problems step by step? ›

Problem-Solving Strategy
  1. Read the word problem. Make sure you understand all the words and ideas. ...
  2. Identify what you are looking for.
  3. Name what you are looking for. ...
  4. Translate into an equation. ...
  5. Solve the equation using good algebra techniques.
  6. Check the answer in the problem. ...
  7. Answer the question with a complete sentence.

What is the free app that solves math equations? ›

Photomath is known worldwide for helping millions of learners to learn, practice, and understand math – one step at a time. Scan any math problem with the Photomath app to get step-by-step explanations with accurate solutions and a variety of teacher-approved methods.

Can ChatGPT solve math problems? ›

while ChatGPT may appear capable of solving simple arithmetic and some algebraic equations, it regularly fails with more complex math problems. This inability to solve math problems may seem paradoxical because our calculators and computers have been successfully helping us solve math problems for over 50 years.

What is the easiest method to solve systems of equations? ›

The Matrix method is the easiest way to solve a set of linear equations, because it is straightforward and a step-by-step method, and it boils down to the same thing as the elimination method that most people are familiar with.

How do you solve an equation step by step? ›

The following steps provide a good method to use when solving linear equations.
  1. Simplify each side of the equation by removing parentheses and combining like terms.
  2. Use addition or subtraction to isolate the variable term on one side of the equation.
  3. Use multiplication or division to solve for the variable.

What are the four ways to solve a system of equations? ›

Solving a system of equations requires you to find the value of more than one variable in more than one equation. You can solve a system of equations through addition, subtraction, multiplication, or substitution. If you want to know how to solve a system of equations, just follow these steps.

Can Photomath be trusted? ›

No, Photomath is not a scam. It is a legitimate educational app designed to assist users in solving a wide range of mathematical problems, offering detailed explanations to enhance learning.

What is the disadvantage of Photomath? ›

The greatest concern about this tool is that it raises the possibility of academic cheating, and may send kids a message to take the easy route when it comes to learning.

Does Photomath give accurate answers? ›

Photomath is using cutting edge AI-powered solving and recognition capabilities, that is why most of our solutions are to the point, and the issue might be in the incorrectly scanned problem. If the result is wrong, first check that the math problem you scanned is the same as the one recognized by Photomath.

How do you solve systems step-by-step? ›

Solving systems of equations by substitution follows three basic steps. Step 1: Solve one equation for one of the variables. Step 2: Substitute this expression into the other equation, and solve for the missing variable. Step 3: Substitute this answer into one of the equations in order to solve for the other variable.

What is the golden rule for solving equations? ›

Golden Rule of Algebra: “Do unto one side of the equal sign as you will do to the other…” **Whatever you do on one side of the equal sign, you MUST do the same exact thing on the other side. If you multiply by -2 on the left side, you have to multiply by -2 on the other.

What is the website that solves any math problem? ›

Wolfram|Alpha has broad knowledge and deep computational power when it comes to math. Whether it be arithmetic, algebra, calculus, differential equations or anything in between, Wolfram|Alpha is up to the challenge.

Is Mathway step by step free? ›

Mathway provides answers to your problems completely free of charge. For step-by-step solutions, an optional monthly or annual subscription is available.

What is the best math website for free? ›

Top 10 Free Math Websites of All Time
  • Cliffs Notes.
  • Khan Academy.
  • Art of Problem Solving.
  • SumDog.
  • Greg Tang Math.
  • Illuminations.
  • Cool Math.
  • Hot Math.

Is there a free math help site? ›

GreeneMath.com exists to offer free math help to anyone with an internet connection! Our goal is to provide a classroom-like experience, guiding students step by step through each topic. We don't replace traditional classrooms, but rather we strive to help students transcend them.

Does Photomath give steps? ›

Photomath is a powerful math teaching app that gives students solutions to math problems as well as the steps taken to achieve the solution. The app uses the camera on your phone or tablet to view written or printed math problems then immediately returns the solution with each individual step explained.

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