Simultaneous Solutions

 

The simultaneous equations consists of two are three variables and it’s called as system of equations .Here the simultaneous solutions can be viewed in many techniques like substitution methods, simultaneous methods. To determine any equation the problem is solved in elimination process for getting the required answer. Let we see about the problems to find the required simultaneous solutions.

 


The Simultaneous Solutions can be done in Following Methods
Steps:
From the first equation, equate the y in terms of xInsert the value of y in the second equation.By applying above steps we can find the values for x and y .
Problems Based on Simultaneous Solutions
Determine the simultaneous solutions in the given problem
Example 1:
x+y+z=10; 2x-y+z=2; -x+2y-z=5
Solution:
x + y + z = 10...................... (1)
2x - y + z = 2........................ (2)
-x + 2y - z = 5....................... (3)
Equating (1) and (3) equation, we getx + y + z = 10-x + 2y - z = 5______________3y = 15

y = 5
Plug  y =5 in equation (1)
x + 5 + z = 10
x + z = 5
z = -x + 5…………… (4)
Substitute y=5 in equation (2)
2x - 5 + z = 2
2x + z = 7
z = -2x + 7………………..(5)
By equating (4) & (5) we get,
-x + 5 = -2x + 7
x = 2
z = -2(2) + 7
= -4 + 7
= 3
Hence the simultaneous solutions :
x = 2
y = 5
z = 3
Determine the simultaneous solutions in the given problem
Example 2:
x - y = 14
2x - y = 28
Solution:
x -y =14................(1)
2x -y =28.............. (2)
Step 1:
y =x-14............. (3)
Step 2:
Substitute 3 in 2
2x-(x-14) =28
2x - x+14 =28
x+14 =28
x =28-14
x=14
Step 3:
Put x =14 in equation 1
x -y =14
14-y =14
y =0
Hence the simultaneous solutions :
x=14
y=0
Determine the simultaneous solutions in the given problem

Example 3:
2x + 3y =-4 and y = x - 3
Solution:
2x+3y = -4 ------------ (1)
y=x-3        --------------(2)
Insert y= x-3 in equation 1
2x+ 3y = -4
2x + 3(x-3) = -4
2x + 3x-9 = -4
5x- 9 = -4
5x = -4+9
5x = 5
x=5/5
x=1
Insert in x=1 in y = x-3
y = x-3 = 1-3
y = -2.
Hence the simultaneous solutions:
x = 1
y = -2