Solve the following system:
{2 x + 3 y = 13 | (equation 1)
12 x - 3 y = -2 | (equation 2)
Swap equation 1 with equation 2:
{12 x - 3 y = -2 | (equation 1)
2 x + 3 y = 13 | (equation 2)
Subtract 1/6 × (equation 1) from equation 2:
{12 x - 3 y = -2 | (equation 1)
0 x+(7 y)/2 = 40/3 | (equation 2)
Multiply equation 2 by 6:
{12 x - 3 y = -2 | (equation 1)
0 x+21 y = 80 | (equation 2)
Divide equation 2 by 21:
{12 x - 3 y = -2 | (equation 1)
0 x+y = 80/21 | (equation 2)
Add 3 × (equation 2) to equation 1:
{12 x+0 y = 66/7 | (equation 1)
0 x+y = 80/21 | (equation 2)
Divide equation 1 by 12:
{x+0 y = 11/14 | (equation 1)
0 x+y = 80/21 | (equation 2)
x = 11/14 and y = 80/21
+128475 2x+3y=13 ⇒ 3y = 13 - 2x (1)
12x-3y=-2 ⇒ 3y = 2 + 12x (2)
Set (1) = (2)
13 - 2x = 2 + 12x add 2x to both sides, subtract 2 from both sides
11 = 14x divide both sides by 14
11/ 14 = x
Putting this into (1), we have
3y = 13 - 2 (11/ 14)
3y = 13 - 11/7 get a common denominator
3y = 91/7 - 11/7
3y = 80/7 divide both sides by 3
y = 80/ 21
