4 - 4y = - 2

- 9x - 4y = - 3

x = - 1/3, y = 3/2

Step-by-step explanation:

Solve the following system:

{4 - 4 y = - 2

-9 x - 4 y = - 3

Express the system in standard form:

{0 - 4 y = - 6

-9 x - 4 y = - 3

Express the system in matrix form:

(0 | - 4

-9 | - 4) (x

y) = (-6

-3)

Write the system in augmented matrix form and use Gaussian elimination:

(0 | - 4 | - 6

-9 | - 4 | - 3)

Swap row 1 with row 2:

(-9 | - 4 | - 3

0 | - 4 | - 6)

Multiply row 1 by - 1:

(9 | 4 | 3

0 | - 4 | - 6)

Divide row 2 by - 2:

(9 | 4 | 3

0 | 2 | 3)

Divide row 2 by 2:

(9 | 4 | 3

0 | 1 | 3/2)

Subtract 4 * (row 2) from row 1:

(9 | 0 | - 3

0 | 1 | 3/2)

Divide row 1 by 9:

(1 | 0 | - 1/3

0 | 1 | 3/2)

Collect results:

Answer: {x = - 1/3, y = 3/2