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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).
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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
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- x+y+z=25,\:5x+3y+2z=0,\:y-z=6
- x+2y=2x-5,\:x-y=3
- 5x+3y=7,\:3x-5y=-23
- x^2+y=5,\:x^2+y^2=7
- xy+x-4y=11,\:xy-x-4y=4
- 3-x^2=y,\:x+1=y
- xy=10,\:2x+y=1
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System of 2 linear equations in 2 variables
[1-10] /17 | Disp-Num |
[1] 2022/07/30 09:34 50 years old level / An engineer / Very /
Purpose of useto solve for both variables in 2 equationsComment/RequestThis was very cool, and I love how you arrive at it.[2] 2021/11/08 17:08 Under 20 years old / High-school/ University/ Grad student / Useful /
Comment/RequestMAth is too hard for me[3] 2021/08/12 11:08 50 years old level / High-school/ University/ Grad student / Useful /
[4] 2021/01/28 01:36 Under 20 years old / Elementary school/ Junior high-school student / Very /
Purpose of useStudy GuideComment/RequestVery useful for fast answers on 2 equations.[5] 2021/01/20 11:31 20 years old level / High-school/ University/ Grad student / Useful /
Purpose of useto learn how use it.[6] 2020/12/01 10:17 60 years old level or over / An engineer / Useful /
Purpose of useFor a bridge building projectComment/Requestuseful for engineers[7] 2020/07/23 05:40 Under 20 years old / High-school/ University/ Grad student / Very /
Purpose of useSolving StatsComment/RequestPretty Good[8] 2020/06/23 03:09 Under 20 years old / Elementary school/ Junior high-school student / A little /
Comment/Requestnot able to calculate with root values[9] 2020/03/20 20:46 Under 20 years old / Elementary school/ Junior high-school student / Useful /
Purpose of usemath presentation/stuck on two linear equation[10] 2019/11/23 12:00 Under 20 years old / High-school/ University/ Grad student / Very /
Purpose of useNot to lose time.Thank you for your questionnaire.
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