Algebra ii Math Solutions

Introduction:

The invention of algebra starts with the Greek mathematician Plato. In general, the term algebra defines the constants and variables. The applications of algebra are widely used in day to day life. In general, algebra is classified into algebra 1, algebra ii and college algebra. Algebra ii is advanced topic when compared to algebra i. In this article, we are going to see about algebra ii math solutions.

Algebra ii math solutions examples:


Example 1:

3x + 6y + 9z = 42

9x + 3y + 6z = 33

6x + 9y + 3z = 33,

Solution:

The given equations are,

3x + 6y + 9z = 42 ---------- {i)

9x + 3y + 6z = 33 ---------- (ii)

6x + 9y + 3z = 33 ---------- (iii)

Let’s take first two equations and solve it,

2* equ (i) => 6x + 12y + 18z = 84

3*equ (ii) =>27x + 9y + 18z = 99 (subtract)

-21x + 3y        = -15 equation (iv)

Solve equation (ii) and (iii)

=> 9x + 3y + 6z    = 33

2*equ (iii) =>12x +18y + 6z = 66 (subtract)

-3x -15y          = -33 equation (v)

Equate equation 4 and 5,

-21x + 3y = -15

-3x   -15y = -33

5*equ(iv) => -105x + 15y = -75

=>   -3x    -  15y = -33   (Add)

-108x       = -108

-108x = -108

Divide 108 on both sides,

108x/108 = 108/108

x = 1

Plugging x in equation (iv)

-21(1) +3y = -15

-21 + 3y = -15

Add 21 on both sides,

-21 + 21 + 3y = -15 + 21

3y = 6

Divide 3 on both sides,

3y/3 = 6/3

y = 2

Plugging x and y values in first equation,

3(1) + 6(2) + 9z = 42

3 + 12 + 9z = 42

15 + 9z = 42

Subtract 15 on both sides,

15 + 9z – 15 = 42 – 15

9z = 27

Divide 3 on both sides,

9z/3 = 27/3

z = 3,

The solutions are x = 1, y = 2, z = 3.

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More examples on algebra ii math solutions


Example 2:

Solve: 5x + 9y > 9

Solution:

Arrange the given inequality in slope intercept form,

5x + 9y = 9

Subtract 5x on both sides,

5x + 9y – 5x = 9 – 5x

9y = -5x + 9

Divide 9 on both sides,

9y/9 = -5x/9 + 9/9

y = -0.56x + 1

Put y = 0

0 = -0.56x + 1

Subtract 1 on both sides,

0 – 1 = 0.56x + 1 – 1

-1 = 0.56x

Divide 0.56 on both sides,

-1/0.56 = 0.56x/0.56

-1.78 = x

Put x = 0, to find x.

y = 0 + 1

y = 1

The solutions are x= -0.56, y =1.