SIMULTANEOUS LINEAR EQUATION

LINEAR EQUATIONS

 Thistype of equations have only single variable and one equation line dimension. 

Eg, 2x - 4 =2

Therefore we solve by saying 2x = 2 + 4

2x = 6, now we devide both sides by 2

2x/2 = 6/2

x = 3

  Exercises 

1)   3 - 2x = 7

2) x + 13 + = 5x - 7

3) -3(x - 1) = 9

4) Find the value of x for which ( WAEC)

2x + 3 - x/3 = x + 7

5) solve the equation (WAEC)

3x/4 + x/3 =7/12

 SIMULTANEOUSLINEAR EQUATIONS

 But in simultaneous linear equations, it carry two or three variables with two lines dimensions. Example of simultaneous equations are as follows.

1) 2x² + y = 2 

2) 2x - 5y = 1 and 4x² + 25y² = 41

Solution to the above example

 2x² + y = 2 therefore

2x² = 2 - y 

by deviding both side by 2

we are now left with.

x² = - y then by applying square root to -y. leaving us with x = √(-y ) 

So now our equation will change by  subtitution

2(√(-y))² + y = 2

-2y + y = 2

y = -2.   

 Now our new generated equation is 

2x² + (-2) = 2

2x² = 2 + 2

2x² = 4 . by dividing both side

x² = 2 . x = √ 2

2(√2)² - 2 = 2

2 * 2 - 2 = 2

4 - 2 = 2

2=2.      Hence proved.

2) 

2x - 5y = 1 and 4x² + 25y² = 41

Now 2x - 5y = 1 → eq 1

4x² + 25y² = 41 → eq 2

 From eq 1 

2x = 1 + 5y ⇔ x = (1 + 5y)/2 ⇒ eq 3

now we subtitute the value of x in eq 2

4 × [(1 + 5y)/2]² + 25y² = 41

(1 + 5y)² = (1 + 5y)(1 + 5y)

(1 + 5y +5y + 25y²) ⇔ (1+ 10y + 25y²)

4[(1 + 10y + 25y²)/4] + 25y² = 41

4 × 1/4( 1+ 10y + 25y²) + 25y² = 41

 letscollect the like term

10y + 25y² + 25y² = 41 - 1

10y + 50y² = 40

  50y² + 10y - 40 = 0

 letsdevide both side by 10

5y² + y - 4 = 0

(5y - 4)(y + 1) = 0

5y - 4 = 0 ⇔ y = 4/5

y + 1 = 0 ⇔ y = -1

 Taking a look at the value of y, our solution may surely be in pairs

 lets subtitute the value of y into eq 3

 y = 4/5 ~ x = [1 + 5 ( 4/5)]/2 = 

x = 2.5

y = -1 ↘ x = [1 + 5(-1)]/2 = 1- 5 = -2

x = -2

 Now our solution is 

(2.5, 4/5) , (-2 , -1)

Hence proved. The seven laws of indices

 Exercisesconcerning SIMULTANEOUS LINEAR EQUATIONS.

1) 2x + y = 5            2)4x - y = 7

     x² + y² = 25            xy = 15

3) 9x² + 16y² = 52.      4) x + 2y = 2

     3x - 4y = 2.                x² + 2xy = 8

 Soonvideo shall be released explaining more clearly about the concept.