Question

solve the following simultaneous equations 7x-3y=1, 5x-2y=1????​

Answer 1

Step-by-step explanation:

Given :-

7x-3y=1, 5x-2y=1

To find :-

Solve the following simultaneous equations

Solution :-

Given pair of linear equations in two variables are

7x-3y = 1 -----------(1)

5x-2y = 1 ----------(2)

=>5x = 1+2y

=> x = (1+2y)/5 ----(3)

On Substituting the value of x in (1) then

=> 7[(1+2y)/5] - 3y = 1

=> [(7+14y)/5]-3y = 1

=> [(7+14y)-(3y×5)]/5 = 1

=>(7+14y-15y)/5 = 1

=> (7-y)/5 = 1

=> 7-y = 1×5

=> 7-y = 5

=> -y = 5-7

=> -y = -2

=>y = 2

On Substituting the value of y in (3)

x = (1+2y)/5

=> x = [1+2(2)]/5

=> x = (1+4)/5

=> x = 5/5

=> x = 1

Therefore, x = 1 and y = 2

Answer:-

The solution for the given problem is (1,2)

Check:-

If x = 1 and y = 2 then

LHS = 7x-3y

=> 7(1)-3(2)

=> 7-6

=> 1

=> RHS

LHS = RHS is true for x = 1 and y = 2

LHS = 5x-2y

=> 5(1)-2(2)

=> 5-4

=>1

=> RHS

LHS = RHS is true for x=1 and y = 2

Used Method:-

• Method of Substitution.