Question

Find the value of a and b, if x = 2, y = 1 is a solution of 2x + 3y = a and x + y = b.​

Answer 1

Given,
x= 2 and y= 1

Equation = (2x + 3y = a)...(i) ,

(x + y = b)...(ii)

Putting the value of x and y in equation (i), we get

2x + 3y = a (Since, x = 2 and y = 1)
2(2) + 3(1) = a
4 + 3 = a
7 = a
Hence, a = 7.

Putting the value of x and y in equation (ii), we get

x + y = b ( Since, x = 2 and y = 1)
2 + 1 = b
3 = b
Hence, b = 3.

Glad to help.

Answer 2

Concept

The solution of an equation is a number that can be used instead of a variable to create a true numeric statement.

Given

We have given two equations which are 2x + 3y = a .....(1)

and x + y = b  ...(2)  and their solution x=2, y=1

Find

We are asked to determine the value of 'a' and 'b' in the given equations.

Solution

If x = 2 and y = 1 is the solution of given equations then, it must satisfy the equations .

Putting x = 2 and y = 1 in equation (1), we get

         $2(2)+3(1)=a\\4+3=a\\a=7$

Putting x = 2 and y = 1 in equation (2), we get

   $2+1=b\\b=3$

Hence, the value of 'a' and 'b' in the given equation are 7 and 3 respectively .

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