Answer:
x = 7 . y = 13/3
Explanation:
Solve the following system:
{y = x/3 + 2
y = (4 x)/3 - 5
Express the system in standard form:
{-x/3 + y = 2
-(4 x)/3 + y = -5
Express the system in matrix form:
(-1/3 | 1
-4/3 | 1)(x
y) = (2
-5)
Write the system in augmented matrix form and use Gaussian elimination:
(-1/3 | 1 | 2
-4/3 | 1 | -5)
Swap row 1 with row 2:
(-4/3 | 1 | -5
-1/3 | 1 | 2)
Subtract 1/4 × (row 1) from row 2:
(-4/3 | 1 | -5
0 | 3/4 | 13/4)
Multiply row 1 by 3:
(-4 | 3 | -15
0 | 3/4 | 13/4)
Multiply row 2 by 4:
(-4 | 3 | -15
0 | 3 | 13)
Divide row 2 by 3:
(-4 | 3 | -15
0 | 1 | 13/3)
Subtract 3 × (row 2) from row 1:
(-4 | 0 | -28
0 | 1 | 13/3)
Divide row 1 by -4:
(1 | 0 | 7
0 | 1 | 13/3)
Collect results:
Answer: {x = 7 . y = 13/3