Solve the following systems of equations:
152x - 378y = -74
-378x + 152y =-604
Answers
Concept :
When the coefficients of x and y in one equation interchanged in the other:
Step 1. Add the given equations and from it obtain an equation of the form x + y = a.
Step 2. Subtract the given equations and from it obtain an equation of the form x - y = b.
Now , x + y = a and x - y = b can be solved easily.
SOLUTION :
152x - 378y = – 74………….(1)
-378x +152y = – 604………..(2)
On Adding Equation 1 and 2 :
152x - 378y = – 74
-378x +152y = – 604
-----------------------------
-226x -226y = - 678
-226(x+y ) = - 678
x + y = - 678/- 226
x + y = 3 ……………….(3)
On Subtracting equation 1 and 2 :
152x - 378y = – 74
-378x +152y = – 604
(+) (-) (+)
-----------------------------
530x - 530y = 530
530 (x - y ) = 530
x - y = 530/530 = 1
x - y = 1……………….(4)
On adding equation 3 and 4 :
x + y = 3
x - y = 1 [By elimination method]
--------------
2x = 4
x = 4/2
x = 2
On substituting x = 2 in eq 3 :
x + y = 3
2 + y = 3
y = 3-2
y = 1
Hence ,the solution of the given system of equation is x = 2 and y = 1.
Hope this answer will help you…
Some more questions from this chapter :
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Hey !
152x - 378y= -74 ----> [ 1 ]
-378x+152y = -604 ----> [ 2 ]
Adding equation 1 and 2
====>
-226x + -226y = -678
x + y = 3 -----> [3]
Now ,
Subtracting equation 1 from 2 ,
-530x + 530y = -530
530y - 530 x = -530
x - y = 1 ----> [ 4 ]
Adding equation 3 and 4
2x = 4
x = 4/2
x = 2
Lets put this value of x in equation 3
2 + y = 3
y = 3 - 2
y = 1