Math

Solve each system by using the elimination method. Make sure to write your answer in (x,y) form.

1.) 3x-5y=2

2x+5y=13

2.) 3x+11y=4
-2x-5y=9

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1. 1.)

3 x - 5 y = 2 Add 5y to both sides

3 x - 5 y + 5 y = 2 + 5 y

3 x = 2 + 5 y Subtract 2 to both sides

3 x - 2 = 2 + 5 y - 2

3 x - 2 = 5 y

5 y = 3 x - 2

2 x + 5 y = 13

2 x + 3 x - 2 = 13

5 x - 2 = 13 Add 2 to both sides

5 x - 2 + 2 = 13 + 2

5 x = 15 Divide both sides by 5

5 x / 5 = 15 / 5

x = 3

3 x - 5 y = 2

3 * 3 - 5 y = 2

9 - 5 y = 2 Add 5 y to both sides

9 + 2 - 5 y + 5 y = 2 + 5 y

9 = 2 + 5 y Subtract 2 to both sides

9 - 2 = 2 + 5 y - 2

7 = 5 y

5 y = 7 Divide both sides by 5

5 y / 5 = 7 / 5

y = 7 / 5

x = 3 , y = 7 / 5

In ( x , y ) form :

( 3 , 7 / 5 )

2.)

3 x + 11 y = 4 Subtract 3 x to both sides

3 x + 11 y - 3 x = 4 - 3 x

11 y = 4 - 3 x Divide both sides by 11

11 y / 11 = ( 4 - 3 x ) / 11

y = ( 4 - 3 x ) / 11

- 2 x - 5 y = 9 Multiply both sides by -1

- 2 x * ( - 1 ) - 5 y * ( - 1 ) = 9 * ( - 1 )

2 x + 5 y = - 9

2 x + 5 * ( 4 - 3 x ) / 11 = - 9

2 x * 11 / 11 + 5 * ( 4 - 3 x ) / 11 = - 9

22 x / 11 + ( 20 - 15 x ) / 11 = - 9

22 x / 11 + 20 / 11 - 15 x / 11 = - 9

7 x / 11 + 20 / 11 = - 9 Multiply both sides by 11

7 x * 11 / 11 + 20 * 11 / 11 = - 9 * 11

7 x + 20 = - 99 Subtract 20 to both sides

7 x + 20 - 20 = - 99 - 20

7 x + 20 - 20 = - 99 - 20

7 x = - 119 Divide both sides by 7

7 x / 7 = - 119 / 7

x = - 17

3 x + 11 y = 4

3 * ( - 17 ) + 11 y = 4

- 51 + 11 y = 4 Add 51 to both sides

- 51 + 11 y + 51 = 4 + 51

11 y = 55 Divide both sides by 11

11 y / 11 = 55 / 11

y = 5

x = - 17 , y = 5

In ( x , y ) form :

( - 17 , 5 )

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