# Simultaneous Equations, Non Linear Equations and Equations with 3 unknown pronumerals

• Feb 27th 2009, 03:22 PM
Needhelpatmaths
Simultaneous Equations, Non Linear Equations and Equations with 3 unknown pronumerals
I have these exercises for homework but I dont understand them, I have read the examples but I can't comprehend how the examples work.

• Feb 27th 2009, 03:28 PM
mr fantastic
Quote:

Originally Posted by Needhelpatmaths
I have these exercises for homework but I dont understand them, I have read the examples but I can't comprehend how the examples work.

If you expect to get help you will need to post the actual questions.
• Feb 27th 2009, 03:37 PM
Needhelpatmaths
Right
Ok I will provide a sample questionof each:

Simultaneous Equations:

3a + 2b = 5 and 2a - b = -6

Non Linear Equations:

xy = 6 and x + y = 5

Equations with 3 Unknown Variables:

a - b + c = 7 , a + 2b - c = -4 and 3a - b - c = 3
• Feb 27th 2009, 07:05 PM
mr fantastic
Quote:

Originally Posted by Needhelpatmaths
Ok I will provide a sample questionof each:

Simultaneous Equations:

3a + 2b = 5 and 2a - b = -6

Mr F says:

3a + 2b = 5 .... (1)
2a - b = -6 .... (2)

Multiply equation (2) by 2 and add it to equation (1): 7a = -7 => a = -1.

Substitute a = -1 into either equation and solve for b.

Non Linear Equations:

xy = 6 and x + y = 5

Mr F says:

xy = 6 .... (1)
x + y = 5 => y = 5 - x .... (2)

Substitute equation (2) into equation (1):

x(5 - x) = 6 => 5x - x^2 = 6 => x^2 - 5x + 6 = 0.
Therefore x = 2, 3.

Substitute the values of x into equation (2) and solve for y.

Equations with 3 Unknown Variables:

a - b + c = 7 , a + 2b - c = -4 and 3a - b - c = 3

Mr F says:

a - b + c = 7 => c = 7 - a + b.... (1)
a + 2b - c = -4 .... (2)
3a - b - c = 3 .... (3)

Substitute equation (1) into equations (2) and (3) and simplify:

2a + b = 3 .... (A)
2a - b = 5 .... (B)

Add equations (A) and (B) together: 4a = 8 therefore a = 2.

Substitute a = 2 into equation (A) or (B) and solve for b. Then substitute the values of a and b into equation (1) and solve for c.

..