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