Question

(a) Prove that the pair of linear equations 3/2x+5/2y=7
and 9x -- 10y = 14 is consistent. Find its solution by
the method of cross multiplication.​

Answer 1

It's a cross multiply method .

And I hope this difficulty is clear .

Answer 2

Answer:

The correct answer is, x = 14/5 and y = 28/25

The given pair of linear equations are consistent. The steps for the same are given below.

Step-by-step explanation:

Given,

3x/2 + 5y/2 = 7

which can be written as

3x/2 + 5y/2 - 7 = 0

or ,

3x +5y - 14 = 0          ...equation(1)

and,

9x - 10y = 14

which can be written as,

9x - 10y - 14 = 0         ...equation(2)

Now, Linear equations are of format ax ± by ± c =0

∴

In equation (1)

a1= 3, b1= 5, c1=-14

and in equation (2)

a2= 9, b2=-10, c2 = - 14

Comparing ratios of the coefficients:

a1/b1 = 3/5 is not equal to a2/b2 = 9/-10,

Since, their slopes are different, the pair of linear equations is consistent.

Rule of cross multiplication:

x/(b1c2 - c2b1) = y/(c1a2 - c2a1) = 1/(a1b2 - a2b1)

Substituting all values of coefficients:

x/(-70-140) = y/(-126+42)= 1/(-30-45)

x/210 = y/84 = 1/75

x= 210/75= 14/5

y = 84/75= 28/25

Hence the value of x is 14/5 and the value of y is 28/25.

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