How to solve the question using elimination method

Question

question 1: 2x+y=3
3x+2y=6

question 2: m-3n=11
2m=5n+19

Answer 1

question 1: 2x+y=3 _______ (1)
                    3x+2y=6 _______(2)

Elimination method

(1)*2 - (2)⇒ 4x+2y = 6

                  3x+2y = 6

                 (-)   (-)    (-)

                 __________

                  x = 0

x=0 in (1)

2*0+y = 3

y = 3

question 2: m-3n=11
                 2m=5n+19

                 m-3n = 11_______ (!)

                2m-5n = 19________ (2)

(1)*2-(2) ⇒2m-6n = 22

                 2m-5n  = 19

                (-)   (+)    (-)

              ____________

                        -n = 3

                         n =- 3

n=-3 in (!)

m-3*-3 = 11

m+9 = 11

m = 2

check:

x = 0, y = 3 in question1 (1)⇒2x+y = 3

                               2*0+3 = 3

                              3 = 3

m=2,n = -3 in question2 (1)⇒m-3n = 11

                               2-3*-3 = 11 

                              2+9 = 11

                                 11 = 11

Answer 2

Question1

2x + y = 3 ------------ Eq (1)

3x + 2y = 6 ----------- Eq (2)

To Eliminate variable y by multiplying the equation 1 by 2 and subtract it from equation 1.

4x + 2y = 6

3x + 2y = 6

--------------

x = 0

Substitute x = 0 in equation 1.

2 * 0 + y = 3

y = 3

Solution is (0, 3).

Question2

m - 3n = 11 ------------ Eq (1)

2m = 5n + 19 ----------- Eq (2)

Subtract  5n from each side.

2m - 5n = 5n - 5n + 19

2m - 5n =  19 ----------- Eq (3)

To Eliminate variable y by multiplying the equation 1 by 2 and subtract it from equation 1.

2m - 5n =  19

2m - 6n = 22

--------------

 n = - 3.

Substitute n = - 3  in equation 1.

m - 3 * ( - 3) = 11

m + 9 = 11

Subtract 9 from each side.

m + 9 - 9  = 11 - 9

m = 2

Solution is (2, - 3).