This solver (calculator) will try to solve a system of 2, 3, 4, 5 equations of any kind, including polynomial, rational, irrational, exponential, logarithmic, trigonometric, hyperbolic, absolute value, etc. It can find both the real and the complex solutions. To solve a system of linear equations with steps, use the system of linear equations calculator. Enter a system of equations: Comma-separated, for example, Solve for (comma-separated): Leave empty for automatic determination, or specify variables like If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.
System of Equations CalculatorStep-by-step calculator for systems of equations. What do you want to calculate? Systems of Equations Calculator is a calculator that solves systems of equations step-by-step. Example (Click to view)x+y=7; x+2y=11 Try it now
About MathPapa Learn how to use the Algebra Calculator to solve systems of equations. Example ProblemSolve the following system of equations: How to Solve the System of Equations in Algebra CalculatorFirst go to the Algebra Calculator main page. Type the following:
Try it now: x+y=7, x+2y=11 Clickable DemoTry entering x+y=7, x+2y=11 into the text box.  After you enter the system of equations, Algebra Calculator will solve the system x+y=7, x+2y=11 to get x=3 and y=4. More ExamplesHere are more examples of how to solve systems of equations in Algebra Calculator. Feel free to try them now.
Need Help?Please feel free to Ask MathPapa if you run into problems. Related Articles
This calculator solves system of three equations with three unknowns (3x3 system). The calculator will use the Gaussian elimination or Cramer's rule to generate a step by step explanation. examples Solve by using Gaussian elimination: $$ \begin{aligned} x + 2y - z & = 2 \\[2ex] x - y + 2z & = 5 \\[2ex] 2x + 2y + 2z & = 12 \end{aligned} $$ Solve by using Cramer's rule $$ \begin{aligned} -x + \frac{2}{3}y - 2z & = 2 \\[2ex] 5x + 7y - 5z & = 6 \\[2ex] \frac{1}{4}x + y - \frac{1}{2}z & = 2 \end{aligned} $$ About Cramer's ruleThis calculator uses Cramer's rule to solve systems of three equations with three unknowns. The Cramer's rule can be stated as follows: Given the system: $$ \begin{aligned} a_1x + b_1y + c_1z = d_1 \\ a_2x + b_2y + c_2z = d_2 \\ a_3x + b_3y + c_3z = d_3 \end{aligned} $$ with
then the solution of this system is:
Example: Solve the system of equations using Cramer's rule $$ \begin{aligned} 4x + 5y -2z= & -14 \\ 7x - ~y +2z= & 42 \\ 3x + ~y + 4z= & 28 \\ \end{aligned} $$ Solution: First we compute $ D,~ D_x,~ D_y $ and $ D_z $. $$ \begin{aligned} & D~~ = \left|\begin{array}{ccc} {\color{blue}{4}} & {\color{red}{~5}} & {\color{green}{-2}} \\ {\color{blue}{7}} & {\color{red}{-1}} & {\color{green}{~2}} \\ {\color{blue}{3}} & {\color{red}{~1}} & {\color{green}{~4}} \end{array}\right| = -16 + 30 - 14 - 6 - 8 - 140 = -154\\ & D_x = \left|\begin{array}{ccc} -14 & {\color{red}{~5}} & {\color{green}{-2}} \\ ~42 & {\color{red}{-1}} & {\color{green}{~2}} \\ ~28 & {\color{red}{1}} & {\color{green}{~4}} \end{array}\right| = 56 + 280 - 84 - 56 + 28 - 840 = -616\\ & D_y = \left|\begin{array}{ccc} {\color{blue}{4}} & -14 & {\color{green}{-2}} \\ {\color{blue}{7}} & ~42 & {\color{green}{~2}} \\ {\color{blue}{3}} & ~28 & {\color{green}{~4}} \end{array}\right| = 672 - 84 - 392 + 252 - 224 + 392 = 616\\ & D_Z = \left|\begin{array}{ccc} {\color{blue}{4}} & {\color{red}{~5}} & -14 \\ {\color{blue}{7}} & {\color{red}{-1}} & ~42 \\ {\color{blue}{3}} & {\color{red}{~1}} & ~28 \end{array}\right| = -112 + 630 - 98 - 42 - 168 - 980 = -770\\ \end{aligned} $$ Therefore, $$ \begin{aligned} & x = \frac{D_x}{D} = \frac{-616}{-154} = 4 \\ & y = \frac{D_y}{D} = \frac{ 616}{-154} = -4 \\ & z = \frac{D_z}{D} = \frac{-770}{-154} = 5 \end{aligned} $$ Note: You can check the solution using above calculator Search our database of more than 200 calculators 227 990 771 solved problems How do you solve a system of equation with 3 variables?To solve a system of three equations in three variables, we will be using the linear combination method. This time we will take two equations at a time to eliminate one variable and using the resulting equations in two variables to eliminate a second variable and solve for the third.
|
How to solve system of equations with 3 variables calculator
Related Posts
Copyright © 2024 kemunculan Inc.
