Solve 2 by 2 system of equations with matrices calculator

This calculator solves Systems of Linear Equations using Gaussian Elimination Method, Inverse Matrix Method, or Cramer's rule. Also you can compute a number of solutions in a system of linear equations (analyse the compatibility) using Rouché–Capelli theorem.

Enter coefficients of your system into the input fields. Leave cells empty for variables, which do not participate in your equations. To input fractions use /: 1/3.

• 2x-2y+z=-3 x+3y-2z=1 3x-y-z=2

Our online expert tutors can answer this problem

Get step-by-step solutions from expert tutors as fast as 15-30 minutes. Your first 5 questions are on us!

Number Line

Our online expert tutors can answer this problem

Get step-by-step solutions from expert tutors as fast as 15-30 minutes. Your first 5 questions are on us!

Number Line

• Math Calculator
• Calculators
• Notes
• Games
• Unit Converter

• Algebra
• Geometry
• Pre-Calculus
• Calculus
• Linear Algebra
• Discrete Math
• Probability/Statistics
• Linear Programming

Solve the system of linear equations step by step

This calculator will solve the system of linear equations of any kind, with steps shown, using either the Gauss-Jordan elimination method, the inverse matrix method, or Cramer's rule.

Related calculator: System of Equations Calculator

Comma-separated, for example, x+2y=5,3x+5y=14.

Leave empty for autodetection or specify variables like x,y (comma-separated).

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.

Your Input

Solve $$$\begin{cases} 5 x - 2 y = 1 \\ x + 3 y = 7 \end{cases}$$$ for $$$x$$$, $$$y$$$ using the Gauss-Jordan Elimination method.

Solution

Write down the augmented matrix: $$$\left[\begin{array}{cc|c}5 & -2 & 1\\1 & 3 & 7\end{array}\right]$$$.

Perform the Gauss-Jordan elimination (for steps, see Gauss-Jordan elimination calculator): $$$\left[\begin{array}{cc|c}5 & -2 & 1\\0 & \frac{17}{5} & \frac{34}{5}\end{array}\right]$$$.

Back-substitute:

$$$y = \frac{\frac{34}{5}}{\frac{17}{5}} = 2$$$

$$$x = \frac{1 - \left(-2\right) \left(2\right)}{5} = 1$$$

Answer

$$$x = 1$$$A

$$$y = 2$$$A