Problem to solve
Solve \[-\frac{2}{3}x+5y=4\], \[7x-5y=4\]
Solution
STEP 1
Solve the following system:
{5 y - (2 x)/3 = 4
-5 y + 7 x = 4
STEP 2
Express the system in matrix form:
(-2/3 | 5
7 | -5)(x
y) = (4
4)
STEP 3
Write the system in augmented matrix form and use Gaussian elimination:
(-2/3 | 5 | 4
7 | -5 | 4)
STEP 4
Swap row 1 with row 2:
(7 | -5 | 4
-2/3 | 5 | 4)
STEP 5
Add 2/21 × (row 1) to row 2:
(7 | -5 | 4
0 | 95/21 | 92/21)
STEP 6
Multiply row 2 by 21:
(7 | -5 | 4
0 | 95 | 92)
STEP 7
Divide row 2 by 95:
(7 | -5 | 4
0 | 1 | 92/95)
STEP 8
Add 5 × (row 2) to row 1:
(7 | 0 | 168/19
0 | 1 | 92/95)
STEP 9
Divide row 1 by 7:
(1 | 0 | 24/19
0 | 1 | 92/95)
STEP 10
Collect results:
Answer: | 
 | {x = 24/19
y = 92/95