solve and check 3x+5y=3 and -x+2y=10

Question

3x+5y=3 and -x+2y=10.

Answer 1

Substitution method :

The equations are

3x  + 5y = 3   ---------> (1)

- x  + 2y = 10 ---------> (2)

Solve for x from (2)

- x  + 2y = 10

Add x to each side.

- x  + 2y  + x= 10 + x

2y  = 10 + x

Subtract 10 from each side.

⇒ x  = 2y - 10.

Substitute the value of x in equation (1).

3(2y - 10) + 5y = 3

6y - 30 +5y = 3

11y - 30 = 3

Add 30 to each side.

11y = 33

Divide to each side by 11.

⇒ y = 3.

Substitute y = 3 in (2).

- x  + 2(3) = 10

- x  + 6 = 10

Subtract 6 from each side.

- x   = 10 - 6 = 4

⇒ x = - 4.

Solution of given system is x = -4 and y = 3.

Check :

Substitute x = -4 and y = 3 in (1).

.

The above statement is true,so x = -4 and y = 3 are the solutions of the given system.