Problem to solve
Solve \[3y+5x+1-2y=2y-3\], \[3y-2+5x=2x-3y+2\]
Solution
STEP 1
Solve the following system:
{y + 5 x + 1 = 2 y - 3
3 y + 5 x - 2 = -3 y + 2 x + 2
STEP 2
Express the system in standard form:
{-y + 5 x = -4
6 y + 3 x = 4
STEP 3
Express the system in matrix form:
(5 | -1
3 | 6)(x
y) = (-4
4)
STEP 4
Solve the system with Cramer's rule:
x = -4 | -1
4 | 6/5 | -1
3 | 6 and y = 5 | -4
3 | 4/5 | -1
3 | 6
STEP 5
Evaluate the determinant 5 | -1
3 | 6 = 33:
x = -4 | -1
4 | 6/33 and y = 5 | -4
3 | 4/33
STEP 6
Evaluate the determinant -4 | -1
4 | 6 = -20:
x = (-20)/33 and y = 5 | -4
3 | 4/33
STEP 7
Evaluate the determinant 5 | -4
3 | 4 = 32:
Answer: | 
 | x = (-20)/33 and y = 32/33