Elimination

Solve the following system:
{4 x+5 y = 6 |     (equation 1)
6 x-7 y = -20 |     (equation 2)
Swap equation 1 with equation 2:
{6 x-7 y = -20 |     (equation 1)
4 x+5 y = 6 |     (equation 2)
Subtract 2/3 × (equation 1) from equation 2:
{6 x-7 y = -20 |     (equation 1)
0 x+(29 y)/3 = 58/3 |     (equation 2)
Multiply equation 2 by 3/29:
{6 x-7 y = -20 |     (equation 1)
0 x+y = 2 |     (equation 2)
Add 7 × (equation 2) to equation 1:
{6 x+0 y = -6 |     (equation 1)
0 x+y = 2 |     (equation 2)
Divide equation 1 by 6:
{x+0 y = -1 |     (equation 1)
0 x+y = 2 |     (equation 2)
Collect results:
Answer: |  x = -1               and                y = 2

4x+5y=6

4x=6-5y

x=(6-5y)/4

Substitute this 'x' into the SECOND equation

6 (6-5y)/4 - 7y = -20

(36-30y)/4 - 7y = -20

36-30y -28y = -80

-58y = -116

y = 2

x=(6-5y)/4 = (6-10)/4 = -1