Answer :
Simultaneous Equation:
7x-8y=11 8x-7y=7
* 7 * -8
49x-56y=77 -64x+56y= -56
On subtracting we get,
- 15x= 21
x= 21/ -15
x= - 7/5
7* -7/5 - 8y =11
-49/5 - 8y=11
-8y = 104/5
y= -51/20
7x-8y=11 8x-7y=7
* 7 * -8
49x-56y=77 -64x+56y= -56
On subtracting we get,
- 15x= 21
x= 21/ -15
x= - 7/5
7* -7/5 - 8y =11
-49/5 - 8y=11
-8y = 104/5
y= -51/20
Concept
Two equations can be solved by eliminating one of the variable terms. This is known as elimination method.
Given
2 equations
7x-8y-11=0
8x-7y-7=0
Find
we need to solve the equations using elimination method
Solution
We have
7x-8y-11=0 and 8x-7y-7=0
multiplying equation 1 by 8 we get
56x - 64y - 88 = 0
and multiplying 2nd equation by 7 we get
56x - 49y - 49 =0
Now we will subtract both the equations so as to eliminate the x term
56x - 64y - 88 - (56x - 49y - 49) = 0
56x - 64y - 88 - 56x + 49y - 49 = 0
- 64y - 88 + 49y + 49 = 0
- 64y - 88 + 49y + 49 = 0
-15y - 39 = 0
-15y = 39
y = -15/39
Thus, x will be
7x - 8(-15/39) - 11 = 0
7x = 11 - 120/39
7x = 309/39
x = 309/273
Thus, on solving the two equations, we get, x = 309/273 and y = -15/39
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