Problem to solve
Solve \[3x+2y=5\], \[-4x+5y=2\]
Solution
STEP 1
Solve the following system:
{2 y + 3 x = 5
5 y - 4 x = 2
STEP 2
Express the system in matrix form:
(3 | 2
-4 | 5)(x
y) = (5
2)
STEP 3
Solve the system with Cramer's rule:
x = 5 | 2
2 | 5/3 | 2
-4 | 5 and y = 3 | 5
-4 | 2/3 | 2
-4 | 5
STEP 4
Evaluate the determinant 3 | 2
-4 | 5 = 23:
x = 5 | 2
2 | 5/23 and y = 3 | 5
-4 | 2/23
STEP 5
Evaluate the determinant 5 | 2
2 | 5 = 21:
x = 21/23 and y = 3 | 5
-4 | 2/23
STEP 6
Evaluate the determinant 3 | 5
-4 | 2 = 26:
Answer: | 
 | x = 21/23 and y = 26/23