solve by elimination method to find an ordered pair.

Question

7x-y=27
x+9y=77

Answer 1

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Answer 2

7 x - y = 27 Divide both sides by 7

7 x / 7 - y / 7 = 27 / 7

x - y / 7 = 27 / 7

x + 9 y = 77

x + 9 y * 7 / 7 = 77 * 7 / 7

x + 63 y / 7 = 539 / 7

Subtract x - y / 7 = 27 / 7 from equation x + 63 y / 7 = 539 / 7

x + 63 y / 7 = 539 / 7

- x - y / 7 = 27 / 7
________________________

x - x + 63 y / 7 - ( - y / 7 ) = 539 / 7 - 27 / 7

0 + 63 y / 7 + y / 7 = 512 / 7

64 y / 7 = 512 / 7 Multiply both sides by 7

64 y = 512 Divide both sides by 64

64 y / 64 = 512 / 64

y = 8

Substitute x in either of the original equations to get the value of y.

7 x - y = 27

7 x - 8 = 27 Add 8 to both sides

7 x - 8 + 8 = 27 + 8

7 x = 35 Divide both sides by 7

7 x / 7 = 35 / 7

x = 5

Solution :

x = 5 , y = 8

Or an ordered pair ( 5 , 8 )

Answer 3

OR

x + 9 y = 77 Multiply both sides by 7

7 * x + 9 y * 7 = 77 * 7

7 x + 63 y = 539
-
7 x - y = 27
_______________

7 x - 7 x + 63 y - ( - y ) = 539 - 27

0 + 63 y + y = 512

64 y = 512

y = 512 / 64 = 8

x + 9 y = 77

x + 9 * 8 = 77

x + 72 = 77 Subtract 72 to both sides

x + 72 - 72 = 77 - 72

x = 5

( 5 , 8 )