Question

If the product of x^2a-1/y^3b+4 and x^7b-4/y^10-a is x^24/y^19 find the value of a and b

Answer 1

Answer:

a = 4; b = 3

Step-by-step explanation:

For the question to make any sense, we need to add parentheses.

... x^(2a-1)/y^(3b+4) × x^(7b-4)/y^(10-a) = x^24/y^19

Equating exponents, we have ...

... (2a-1) + (7b-4) = 24 . . . . exponent of x in the product

... (3b+4) + (10 -a) = 19 . . . exponent of y in the product

Simplifying these two equations, we get

... 2a +7b = 29

... a -3b = -5

By Cramer's rule, ...

... a = (7·(-5) -(-3·29)/(7·1 -(-3·2)) = 52/13 = 4

... b = (29·1 -(-5·2))/13 = 39/13 = 3

_____

More about Cramer's Rule

If you have the linear equations ...

• ax +by = c
• dx +ey = f

The solutions for the variables x and y can be found directly from the equation coefficients as ...

... x = (bf -ec)/(bd -ea)

... y = (cd -fa)/(bd -ea) . . . . same denominator as for the first equation

Once you recognize the pattern in the products, the formula is not difficult to remember.

___

This is actually the Vedic math version of Cramer's rule. It differs from the usual presentation of Cramer's rule in that both numerator and denominator are negated. This makes the pattern of products easier to remember and gives exactly the same result.