8th Grade Problem Solving

Introduction to 8th grade problem solving:

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. Here we are going to see about 8th grade problem solving and its example problems.                                                                                      Source: Wikipedia

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Example for 8th grade problem solving:


8th grade problem solving example: 1

Solve 3x + 3 = 12

Solution:

Given that 3x + 3 = 12

Subtract the -3 on both sides

3x + 3 – 3 = 12 – 3

3x = 9

Divide both side using 3

`(3x) / 3` = `9 / 3`

x = 3

The solution is x = 3.

8th grade problem solving example: 2

Solve 4x + 3y = 9

5x + 3y = 5

Solution:

Given that   4x + 3y = 9 ------------- (1)

5x + 3y = 5-------------- (2)

Subtract the first equation and second equation

4x + 3y = 9

(`-` )  5x + 3y = 5

_______________

-x = 4

x = - 4

x = - 4 take the value and substitute in equation (1).

4x + 3y = 9 ------------- (1)

x = -4

4(-4) + 3y = 9

-16 + 3y = 9

Add the +16 on both sides

+16 – 16 + 3y = 9 + 16

3y = 25

Divide using 3 on both sides

` (3y) / 3` = `25 / 3`

y = 8.33

The solution is x = -4

y = 8.33

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Example for 8th grade problem solving:


8th grade problem solving example: 3

Solve 6x + 4y = 2

7x + 5y = 3

Solution:

Given that   6x + 4y = 2 ------------- (1)

7x + 5y = 3 ------------- (2)

From these two equations we cannot cancel particular variable

So we need to change this equation at least one variable equal on both equations

(1)   * 5 =   30x + 20y = 10

(2)   * 4 =   28x + 20y = 12

From this equation we can cancel one variable.

30x + 20y = 10

( - ) 28x + 20y = 12

Subtract you can get the value

2x = - 2

Divide using 2 on both sides

x = - 2 / 2

x = -1

x = - 1 take the value and substitute in equation (1).

6x + 4y = 2 ------------- (1)

6(-1) + 4y = 2

-6 + 4y = 2

Add +6 on both sides

+6 – 6 + 4y = 2 + 6

4y = 8

Divide using 4 on both sides

`y / 4` = `8 / 4`

y = 2

The solution is x = -1

y = 2