Problem to solve
Solve \[3x+5y=2\], \[-5x+6y=5\]
Solution
STEP 1
Solve the following system:
{5 y + 3 x = 2 | (equation 1)
6 y - 5 x = 5 | (equation 2)
STEP 2
Swap equation 1 with equation 2:
{-(5 x) + 6 y = 5 | (equation 1)
3 x + 5 y = 2 | (equation 2)
STEP 3
Add 3/5 × (equation 1) to equation 2:
{-(5 x) + 6 y = 5 | (equation 1)
0 x+(43 y)/5 = 5 | (equation 2)
STEP 4
Multiply equation 2 by 5:
{-(5 x) + 6 y = 5 | (equation 1)
0 x+43 y = 25 | (equation 2)
STEP 5
Divide equation 2 by 43:
{-(5 x) + 6 y = 5 | (equation 1)
0 x+y = 25/43 | (equation 2)
STEP 6
Subtract 6 × (equation 2) from equation 1:
{-(5 x)+0 y = 65/43 | (equation 1)
0 x+y = 25/43 | (equation 2)
STEP 7
Divide equation 1 by -5:
{x+0 y = -13/43 | (equation 1)
0 x+y = 25/43 | (equation 2)
STEP 8
Collect results:
Answer: | 
 | {x = -13/43
y = 25/43