Solving Equations with Multiplying Variables

Introduction of solving equations with Multiplying Variables:

Solving equations with Multiplying Variables is the part of algebra, generally the equation consist of three variables we need to find the value of variables. The equations are x+2y+z =3, 2x-y+z = 4 and 4x-2y+3z = 5, here the variable are x, y and z, solving this equation we need to find the value of variable. In this article we shall discuss solving equations with Multiplying Variables with suitable example problems.

Problems in Solving Equations with Multiplying Variables

Simplify and solving equations with Multiplying Variables

Problem(i) x+2y+z = -4, and –x+y+z = 8 and -x+y+2z = 12.

Solution:

Let assume the first equation as x+2y+z = -4---------(1).

Let assume the second equation as –x+y+z = 8-------(2)

Let assume the third equation as –x+y+2z = 12-------(3).

Adding first two equation (1)+(2).

x+2y+z = -4

-x+y+z  = 8

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3y+2z =  4this  is the fourth equation --------------(4).

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Adding first and third equations(1)+(3).

x+2y+z = -4

-x+y+2z = 12

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3y+3z = 8 this is the fifth equation-------------------(5).

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Adding (4) and (5).

3y+2z = 4

3y+3z = 8

-   -       -  

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-z = -4

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z = 4.

Substitute the z value in the fourth equation

3y+2(4) = 4

3y +8 = 4

3y = 4-8

3y = -4 dividing both sides by 3

`(3y)/3` = `-4/3`

y = -1.33.

Here z is 4 and y is -1.33

Substitute the value of  z and y in the first equation

The first equation is

x+2y+z = -4

x+2(-1.33)+4 = -4

x-2.66+4 = -4

x+1.34 = -4.

x = -4-1.34

x = -5.34

Therefore x = -5.34, y = -1.33 and, z = 4.

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Problems in Solving Equations with Multiplying Variables

Simplify and solving equations with Multiplying Variables

Problem(i) 2x-y+z = -4, and x-y+2z = 8 and -x+y+2z = 12.

Solution:

Let assume the first equation as 2x-y+z = -4---------(1).

Let assume the second equation as x-y+2z = 8-------(2)

Let assume the third equation as –x+y+2z = 12-------(3).

Taking the equation two and 3 and adding

x-y+2z = 8

-x+y+2z = 12

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4z  =20

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4z = 20

Dividing both sides by 4

`(4z)/4` = `20/4`

z = 5.

Now substitute z value in the first and second equation

2x-y+5 = -4

2x-y =-4-5

2x-y = -9 is the fourth equation ------------(4).

x-y+2z = 8

x-y+2`xx` 5 = 8

x-y = -10+8

x-y =8-10

x-y = -2 is the fifth equation------------(5).

Adding the equation (4) and (5).

2x-y = -9

x-y = -2

- +    +

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x = -7

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The value of x is -7

Substitute the value of x in the 4 equation

2`xx` -7-y = -9

-14-y = -9

-y = -9+14

-y = 5

y = -5

Therefore x = -7, y = -5, and z=5.