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System of Equations Solver

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System of linear equation is a group of linear equations with a set of variables. A system of linear equation can be in two or three variables, i.e.,

Linear equation with two variables is given by,
Lx + My = N
Ox + Py = Q


Linear equation with three variables is given by,
Lx + My + Nz = O
Px + Qy + Rz = S
Tx + Uy + Vz = W


Here, x, y and z are the three variables.

A solution is a group of variable values that satisfy all set of equations. Solution of a system can have infinite many solution, unique solution or no solution. To solve these system of equation, there are different ways i.e,
  • Substitution method
  • Elimination method
  • Cramer's rule
  • Graphing method
This online system of equation solver finds the solution of the given equations.
 

Steps to Find the System of Equation

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Step 1: Observe the set of equation and choose simplest equation to solve for x and y.

Step 2: Substitute the simplest equation into other equation and solve for either of the variable.

Step 3: After getting the value for one of the variable, find the value of another variable. And check the solution.

Syetem of Equation Solved Problems

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Given below are some of the problems based on system of equation.

Solved Examples

Question 1: Solve the following system of equation,
2x + y = 1
-3x - 2y = -3
Solution:
 
Step 1: Given equation :  
2x + y = 1
-3x - 2y = -3

As first equation is simplest equation, let us consider.
2x + y = 1
y = 1 - 2x

Step 2: Substitute the first equation into second equation to solve for x.
-3x - 2y = -3
-3x - 2(1 - 2x) = -3
-3x - 2 + 4x = -3
x = -3 + 2
x = -1

Step 3: Let us find the value of y by substituting x value in first equation.
2(-1) + y = 1
-2 + y = 1
y = 1 + 2
y = 3

Therefore, the solution for the given equation is (x, y) = (-1, 3).

 

Question 2: Solve the following system of equation,
-x - 3y = -16
-x + 2y = 9
Solution:
 
Step 1 : Given equation :
-x - 3y = -16
-x + 2y = 9

As second equation is simplest equation, let us consider.
-x + 2y = 9
x = 2y - 9

Step 2 : Substitute the first equation into first equation to solve for y.
-x - 3y = -16
-(2y - 9) - 3y = -16
-2y +9 -3y = -16
-5y = -16 - 9
y = $\frac{25}{5}$
y = 5

Step 3 : Let us find the value of x by substituting y value in second equation.
-x + 2y = 9
-x + 2(5) = 9
x = 10 - 9
x = 1

Therefore, the solution for the given equation is (x, y) = (1, 5).