How do solve the following linear system?: 3x-8y=6, 5x+2y=2 3x8y=6,5x+2y=2?

1 Answer
Apr 18, 2018

See a solution process below

Explanation:

3x - 8y = 6 - - - eqn13x8y=6eqn1

5x + 2y = 2 - - - eqn25x+2y=2eqn2

Using elimination method..

5 xx (3x - 8y = 6)5×(3x8y=6)

3 xx (5x + 2y = 2)3×(5x+2y=2)

15x - 40y = 30 - - - eqn315x40y=30eqn3

15x - 6y = 6 - - - eqn415x6y=6eqn4

Subtract eqn3 and eqn4eqn3andeqn4

-34y = 2434y=24

y = - 24/34y=2434

y = - 12/17y=1217

Substitute the value of yy into eqn1eqn1

3x - 8y = 63x8y=6

3x - 8(-12/17) = 63x8(1217)=6

3x + 96/17 = 63x+9617=6

Multiply through by 1717

17(3x) + 17(96/17) = 17(6)17(3x)+17(9617)=17(6)

51x + 96 = 10251x+96=102

51x = 102 - 9651x=10296

51x = 651x=6

x = 6/51x=651

x = 2/17x=217

Hence;

x = 2/17 and y = -12/17x=217andy=1217