**Introduction to learn algebra calculator:**

**Algebra** is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms,
polynomials, equations and algebraic structures. Together with geometry, analysis, topology, combinatorics, and number theory, algebra is one of the main branches of pure mathematics.

Now let us see the problems in learn algebra problems using calculator.

**Problem 1 :**

3x - y = -16---------------------- (1)

2x+8y =-28---------------------- (2)

The above problem can be solved in calculator

The calculator uses equation of 2 by 2 and get the correct result.

The value are entered the values to the calculator solver it functions the system of equations .

**The required answer are** **x = -4, y = -2**

**Problem 2 :**

**Given that :**x + 3y = 7 - - - - - - (1)

2x + y = 4 - - - - - - (2)

The above problem can be solved in calculator :

The calculator uses equation of 2by 2 and get the correct result.

**Let us see the same problem in manually,**

(1) * 2 → 2x + 6y = 14

(2) → 2x + y = 4

Now subtracting the two equations,

*2x + 6y = 14*

0 + 5y = 10

y = 10 / 5

y = 2

Thus, y = 2. Substitute y = 2 in either of the two equations,

2x + y = 4

2x + 2 = 4

2x = 4 - 2

2x = 2

x = 2/2

x = 1

**Answer: x =1 and y =2**

**Given that :**

x - y = -5 --------------------(1)

3x+8y = -48-----------------(2)

The problem can solved in calculator :

**The problem can be solved in manually,**

x - y = -5 --------------------(1)

3x+8y = -48-----------------(2)

**Answer : **

**Step 1:** Rearrange the first equation,

x - y = -5

y = x + 5---------------------(3)

** Step 2:** insert this value in for y =x + 5 into the second equation;

3x + 8(x + 5) = -48

**Step 3:**Expand and simplify the equation:

3x + 8x + 40 = -48

11x = -88

x = -8-----------------------(4)

**Step 4:**

Insert of the value x back into the one of that original equations;

-8 - y = -5

y = -3----------------------------(5)

**The required answer are x = -8, y = -3**

**Solve the equations** : x + 2y + 3z = 14, 3x + y + 2z = 11, 2x + 3y + z = 11.

**Solution :** Let the given equations be identified as follows.

x + 2y + 3z = 14 ......................(1)

3x + y + 2z = 11 .......................(2)

2x + 3y + z = 11..................... (3)

**Consider the equations (1) and (3)**

(1) `=>` x + 2y + 3z = 14

(3) x3 `=>` 6x + 9y + 3z = 33 subtracting

_____________

–5x – 7y = –19

5x + 7y = 19................................. (4)

**Consider the equations (2) and (3)**

(2) `=>` 3x + y + 2z = 11

(3) x2 `=>` 4x + 6y + 2z = 22 subtracting

_______________

–x – 5y = –11

x + 5y = 11........................ (5)

**Consider the equations (4) and (5)**

(4) `=>` 5x + 7y = 19

(5) x5 `=>` 5x + 25y = 55 subtracting

______________

–18y = –36 ; ∴y = 2

**Substitute y = 2 in (5) we get**

x + 5(2) = 11; x + 10 = 11; ∴x = 1

**Substitute x = 1, y = 2 in (3) we get**

2(1) + 3(2) + z = 11; 2 + 6 + z = 11 `=>` z = 3

**The solution is x = 1, y = 2, z = 3.**

The above sum is to learn algebra problem using calculator in simultaneous equation