System of Equations Solver

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**Step 2 :**

**Step 3 :**

A **System of Linear Equations** or systems is a set of linear equations, which contains same set of variables. A system of linear equations in three variables is mostly need to use more variable than single variable to form a condition in many fields. In such a situation we need to use system of equation in order to get solution for the given condition.

When a linear equation has at least one answer, it is reliable. If the system has no solution, then it is non – reliable. When the system has more number of answers, then it is dependent, else it is independent.

**A system of linear equations in two variables is given by: **

**Ax + By = C **

Dx + Ey = F

** A system of linear equations in three variables is given by:**

** Ax + By + Cz = D**

Ex + Fy + Gz = H

Ix + Jy + Kz = LIn a two systems of linear equations we have two unknown variables and we need to calculate those two unknown variables. Similarly in a three systems of linear equations we have three unknown variables and we need to calculate those three unknown variables. A system of linear equations can be solved in the following ways:

**Solving systems of equations calculator **or **System of Equations Calculator** will help us to find the solution for system of linear equations. If the systems of equation are given in the block provided it solves and gives you the value of variable. Hence it acts as a **System of Equations Solver ** or** ordered pair calculator** or **linear system calculator**.

When a linear equation has at least one answer, it is reliable. If the system has no solution, then it is non – reliable. When the system has more number of answers, then it is dependent, else it is independent.

Dx + Ey = F

Ex + Fy + Gz = H

Ix + Jy + Kz = L

**Substitution method****Elimination method****Cramer's rule****Graphing method**

Observe the given equations and select any easiest equation to solve for x = or y =.

Now, substitute the equation comes from the step1 into other equation and then solve for the variable. After getting the value for either of the variable, just put it on the equation ofstep1.

The solution of the variables can be written is an order pair.

Solve the system of equations

x - y = 2

2x - y = 2

**Step 1 :**Consider the first equation: x - y = 2

$\Rightarrow$ x = 2 + y**Step 2 :**Now consider second equation, 2x - y = 2

Substitute x = 2 + y in the above equation.

So, 2(2 + y) - y = 2

$\Rightarrow$ 4 + 2y - y = 2

$\Rightarrow$ 4 + y = 2

$\Rightarrow$ y = 2 - 4 = -2

If we substitute y = -2 in x = 2 + y

then, x = 2 - 2 = 0

**Step 3 :**So, x = 0 and y = -2

The solution is (x, y) = (0, -2).

**Answer :**The solution is (x, y) = (0, -2).

Solve the system of equations

x + 3y = 2

x + 4y = 3

**Step 1 :**Consider the second equation: x + 4y = 3

$\Rightarrow$ x = 3 - 4y**Step 2 :**Now consider first equation, x + 3y = 2

Substitute x = 3 - 4y in the above equation.

So, 3 - 4y + 3y = 2

$\Rightarrow$ 3 -y = 2

$\Rightarrow$ y = 3 - 2

$\Rightarrow$ y = 1

If we substitute y = 1 in x = 3 - 4y

then, x = 3 - 4(1) = 3 - 4 = -1

**Step 3 :**So, x = -1 and y = 1

The solution is (x, y) = (-1, 1).

**Answer :**The solution is (x, y) = (-1, 1).