Question

x+2y=5;2x-3y=8 pair of liner equation in two variables ​

Answer 1

Step-by-step explanation:

Given :-

X+2Y = 5

2X-3Y = 8

To find :-

Solve the pair of linear equations in two variables?

Solution :-

Given pair of linear equations in two variables are

X+2Y = 5 ----------(1)

=> X = 5-2Y -------(2)

And given another equation

2X-3Y = 8 ----------(3)

On Substituting the value of X from (2) in (3)

=> 2(5-2Y) -3Y = 8

=> 10 - 4Y - 3Y = 8

=> 10 - 7Y = 8

=> -7Y = 8-10

=> -7Y = -2

=> Y = -2/-7

=> Y = 2/7

On Substituting the value of Y in (2) then

=> X = 5-2(2/7)

=> X = 5-(4/7)

=> X = (5×7-4)/7

=> X = (35-4)/7

=> X = 31/7

Therefore, X = 31/7 and Y = 2/7

Answer:-

The solution for the pair of linear equations in two variables is ( 31/7 , 2/7 )

Check :-

I) If X = 31/7 and Y = 2/7 then LHS of the first given equation X+2Y

=> (31/7)+2(2/7)

=> (31/7)+(4/7)

=> (31+4)/7

=> 35/7

=> 5

=>RHS

LHS = RHS is true for X = 31/7 and Y = 2/7

2) If X = 31/7 and Y = 2/7 then LHS of the second given equation 2X-3Y

=> 2(31/7)-3(2/7)

=> (62/7)-(6/7)

=> (62-6)/7

=> 56/7

=> 8

=> RHS

LHS = RHS is true for X = 31/7 and Y = 2/7

Verified the given relations in the given problem

Used Method :-

• Substitution method

Points to know:-

There are two types of methods to solve the given pair of linear equations in two variables.

They are :

1) Graphical method

2) Algebraic methods

In Algebraic methods , we use

• Substitution method
• Elimination method
• Reducible to linear equations method
• Cross Multiplication Method