Problem to solve
Solve \[-4x+5y+3=x+4\], \[6x-7y=2y-1\]
Solution
STEP 1
Solve the following system:
{5 y - 4 x + 3 = x + 4 | (equation 1)
-7 y + 6 x = 2 y - 1 | (equation 2)
STEP 2
Express the system in standard form:
{-(5 x) + 5 y = 1 | (equation 1)
6 x - 9 y = -1 | (equation 2)
STEP 3
Swap equation 1 with equation 2:
{6 x - 9 y = -1 | (equation 1)
-(5 x) + 5 y = 1 | (equation 2)
STEP 4
Add 5/6 × (equation 1) to equation 2:
{6 x - 9 y = -1 | (equation 1)
0 x - (5 y)/2 = 1/6 | (equation 2)
STEP 5
Multiply equation 2 by 6:
{6 x - 9 y = -1 | (equation 1)
0 x - 15 y = 1 | (equation 2)
STEP 6
Divide equation 2 by -15:
{6 x - 9 y = -1 | (equation 1)
0 x+y = -1/15 | (equation 2)
STEP 7
Add 9 × (equation 2) to equation 1:
{6 x+0 y = -8/5 | (equation 1)
0 x+y = -1/15 | (equation 2)
STEP 8
Divide equation 1 by 6:
{x+0 y = -4/15 | (equation 1)
0 x+y = -1/15 | (equation 2)
STEP 9
Collect results:
Answer: | 
 | {x = -4/15
y = -1/15