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
y - (3 x)/5 = 5 y + 2
STEP 2
Express the system in standard form:
{(6 x)/5 + (3 y)/2 = 5
-(3 x)/5 - 4 y = 2
STEP 3
Express the system in matrix form:
(6/5 | 3/2
-3/5 | -4)(x
y) = (5
2)
STEP 4
Write the system in augmented matrix form and use Gaussian elimination:
(6/5 | 3/2 | 5
-3/5 | -4 | 2)
STEP 5
Add 1/2 × (row 1) to row 2:
(6/5 | 3/2 | 5
0 | -13/4 | 9/2)
STEP 6
Multiply row 1 by 10:
(12 | 15 | 50
0 | -13/4 | 9/2)
STEP 7
Multiply row 2 by 4:
(12 | 15 | 50
0 | -13 | 18)
STEP 8
Divide row 2 by -13:
(12 | 15 | 50
0 | 1 | -18/13)
STEP 9
Subtract 15 × (row 2) from row 1:
(12 | 0 | 920/13
0 | 1 | -18/13)
STEP 10
Divide row 1 by 12:
(1 | 0 | 230/39
0 | 1 | -18/13)
STEP 11
Collect results:
Answer: | 
 | {x = 230/39
y = -18/13