Problem to solve
Solve \[\frac{6}{5}x+\frac{3}{2}y=5\], \[-\frac{3}{5}x+y=5y+2\]
Solution
STEP 1
Solve the following system:
{(3 y)/2 + (6 x)/5 = 5 | (equation 1)
y - (3 x)/5 = 5 y + 2 | (equation 2)
STEP 2
Express the system in standard form:
{(6 x)/5 + (3 y)/2 = 5 | (equation 1)
-(3 x)/5 - 4 y = 2 | (equation 2)
STEP 3
Add 1/2 × (equation 1) to equation 2:
{(6 x)/5 + (3 y)/2 = 5 | (equation 1)
0 x - (13 y)/4 = 9/2 | (equation 2)
STEP 4
Multiply equation 1 by 10:
{12 x + 15 y = 50 | (equation 1)
0 x - (13 y)/4 = 9/2 | (equation 2)
STEP 5
Multiply equation 2 by 4:
{12 x + 15 y = 50 | (equation 1)
0 x - 13 y = 18 | (equation 2)
STEP 6
Divide equation 2 by -13:
{12 x + 15 y = 50 | (equation 1)
0 x+y = -18/13 | (equation 2)
STEP 7
Subtract 15 × (equation 2) from equation 1:
{12 x+0 y = 920/13 | (equation 1)
0 x+y = -18/13 | (equation 2)
STEP 8
Divide equation 1 by 12:
{x+0 y = 230/39 | (equation 1)
0 x+y = -18/13 | (equation 2)
STEP 9
Collect results:
Answer: | 
 | {x = 230/39
y = -18/13