How do you solve the following system of equations?: 13x+13y=16, 3x + 19y=19?

1 Answer
Oct 22, 2017

x = 57/208, y = 199/208

Explanation:

13x + 13y = 16.....(I)

3x + 19y = 19.....(II)

Rearranging (II) for x for simplicity,

3x = 19 - 19y

impliesx = (19-19y)/3

Substituting for x in (I)

13( (19-19y)/3) + 13y = 16

implies(247 - 247y)/3 + 13y = 16

implies(247-247y+39y)/3 = 16

implies247-208y = 16*3

implies208y = 247 - 48

impliesy = 199/208

Substituting for y in either equation (we'll choose (II)),

3x + 19(199/208) = 19

implies3x = 19 - 3781/208

impliesx = 1/3*((3952 - 3781)/208) = 1/3 * (171/208) = 171/624 = 57/208