Question

(04.03 MC)

Answer 1

Answer:

x = -2 and y = 3

{y = -3 x - 3, y = (3 x)/4 + 9/2} = x = -2 and y = 3

Step-by-step explanation:

Solve the following system:

{6 x + 2 y = -6

3 x - 4 y = -18

Express the system in matrix form:

(6 | 2

3 | -4)(x

y) = (-6

-18)

Solve the system with Cramer's rule:

x = -6 | 2

-18 | -4/6 | 2

3 | -4 and y = 6 | -6

3 | -18/6 | 2

3 | -4

Evaluate the determinant 6 | 2

3 | -4 = -30:

x = -6 | 2

-18 | -4/(-30) and y = 6 | -6

3 | -18/(-30)

Simplify -6 | 2

-18 | -4/(-30):

x = -1/30 -6 | 2

-18 | -4 and y = 6 | -6

3 | -18/(-30)

Simplify 6 | -6

3 | -18/(-30):

x = -(-6 | 2

-18 | -4)/30 and y = -1/30 6 | -6

3 | -18

Evaluate the determinant -6 | 2

-18 | -4 = 60:

x = (-1)/30×60 and y = -(6 | -6

3 | -18)/30

(-1)/30×60 = -2:

x = -2 and y = -(6 | -6

3 | -18)/30

Evaluate the determinant 6 | -6

3 | -18 = -90:

x = -2 and y = (-1)/30×-90

(-1)/30 (-90) = 3:

Answer: x = -2 and y = 3

___________________________________________

Solve the following system:

{y = -3 x - 3

y = (3 x)/4 + 9/2

Express the system in standard form:

{3 x + y = -3

-(3 x)/4 + y = 9/2

Express the system in matrix form:

(3 | 1

-3/4 | 1)(x

y) = (-3

9/2)

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

(3 | 1 | -3

-3/4 | 1 | 9/2)

Add 1/4 × (row 1) to row 2:

(3 | 1 | -3

0 | 5/4 | 15/4)

Multiply row 2 by 4/5:

(3 | 1 | -3

0 | 1 | 3)

Subtract row 2 from row 1:

(3 | 0 | -6

0 | 1 | 3)

Divide row 1 by 3:

(1 | 0 | -2

0 | 1 | 3)

Collect results:

Answer:  {x = -2 , y = 3