The solution of a pair of Linear equations X + 2Y = 55 and 6X - Y =5 is
Answers
Step-by-step explanation:
Let the present age of Aftab = x
And, present age of his daughter is represented as = y
Seven years ago,
Aftab’s age = x – 7
Age of Aftab’s daughter = y – 7
According to the question,
(x – 7) = 7 (y – 7 )
x – 7 = 7 y – 49
x – 7y = – 49 + 7
x – 7y = – 42 … (i)
x = 7y – 42
Putting y = 5, 6 and 7, we get
x = 7 × 5 – 42 = 35 – 42 = – 7
x = 7 × 6 – 42 = 42 – 42 = 0
x = 7 × 7 – 42 = 49 – 42 = 7
Three years from now,
Aftab’s age = x + 3
Age of Aftab’s daughter = y + 3
According to the question,
(x + 3) = 3 (y + 3)
x + 3 = 3y + 9
x – 3y = 9 – 3
x – 3y = 6 … (ii)
x = 3y + 6
Putting, y = – 2, –1 and 0, we get
x = 3 × – 2 + 6 = – 6 + 6 =0
x = 3 × – 1 + 6 = – 3 + 6 = 3
x = 3 × 0 + 6 = 0 + 6 = 6
Algebraic representation
From equation (i) and (ii)
x – 7y = – 42 … (i)
x – 3y = 6 … (ii)
Graphical representation
Answer:X=5 and Y=25
Step-by-step explanation:X+2Y=55
=>Y=55-X/2 (i)
6X-Y=5
=>6X-(55-X/2)=5 (putting the value of y from (i))
=>12X-55+X/2=5
=>13X-55=5x2
=>13X=10+55
=>X=65/13
=>X=5
from (i),
Y=55-X/2
=>Y=55-5/2
=>Y=25