How do you solve the following system?: 16x +13y =7, -19x +15y = -2

2 Answers
Apr 25, 2018

x = 131/7

y = -(2047)/91

Explanation:

  1. 16x+13y = 7
  2. 15y - 19x =-2

In equation 1, make y the subject.

13y = 7-16x -> y = (7-16x)/13

Inject that into equation 2.

15((7-16x)/13) - 19x = -2

Solve for x.

(105-240x)/13 -19x = -2

(105-240x)/13 = 19x - 2

105 -240x = 247x - 26

247x-240x = 105+26

7x = 131

x = 131/7

Inject the value x into the rearranged equation 1 to calculate the value of y.

y = (7-16(131/7))/13

y = -(2047)/91

Apr 25, 2018

x=131/487
y=101/487

Explanation:

16x+13y=7
-19x+15y=-2

Multiply top equation by 15 and second linear equation by 13 to make the values of y the same so they cancel out when subtracted from each other:

240x+195y=105
-247x+195y=-26
which gives:
487x=131 when subtracted from each other.
x=131/487

Substitute x into first original equation:

16(131/487)+13y=7
(2096/487)+13y=7
13y=7-(2096/487)
13y=(1313/487)
y=((1313/487))/13
y=101/487