Question

Solve by elimination:
2x-y=8 and y=5x+3

X-2y=3 and 5x + 3y= 4

Y=4x-7 and 6x+3y= 19

Answer 1

1 ) 2x - y = 8 and y = 5x + 3

Let 2x - y = 8 ------------>(1) and

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

From (1) + (2)

            2x - y = 8

          -5x + y = 3

 -----------------------------------

          - 3x  + 0 = 11

           x  = - 11/3

Multiply 5(1) and 2(2)

5(2x - y = 8) and 2(-5x + y = 3)

10x - 5y = 40 --------------->(3) and

- 10x + 2y = 6 -------------------->(4)

From (3) + (4)

            10x - 5y = 40

         - 10x + 2y = 6

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

           0 - 3y = 46

                y = - 46/3

 

Answer 2

1) x - 2y = 3 and 5x + 3y= 4

Let x - 2y = 3 ---------> (1) and

5x + 3y= 4 -----------> (2)

Multiply 5 × (1)

5x - 10y = 15 ------------->(3)

From (2) and (3)

           5x + 3y =  4

           5x  -10y = 15

       ( - )

 ------------------------------------

            0 + 13y = -11

                     y = -11/13

Multiply 3(1) and 2(2)

          3 x - 6y = 9 ---------->(4)

       10x + 6y= 8 --------------->(5)

From (4) and (5)

                3 x - 6y = 9

              10x + 6y = 8

 ----------------------------------

               13x + 0 = 17

                     x = 17/13

Answer 3

3 ) y = 4x - 7 and 6x + 3y = 19

Let y = 4x - 7 ------------->(1)

6x + 3y = 19 ------------->(2)

Multiply 6(1) and 4 (2)

       - 24x + 6y = - 42

         24x + 12y =  76

 _____________________

           0 + 18y = 34

                        y  = 17/9

Multiply  3(1) and  1(2)

      -12x + 3y = - 21

         6x + 3y = 19

( - )

___________________

     -18x + 0 =  - 40

               x = 20/9