4.5x - 2y = 15

3x - y = 10

(answer as a combined pair)

x = 10/3, y = 0

Step-by-step explanation:

Solve the following system:

{4.5 x - 2 y = 15

3 x - y = 10

In the first equation, look to solve for x:

{4.5 x - 2 y = 15

3 x - y = 10

4.5 x - 2 y = (9 x) / 2 - 2 y:

(9 x) / 2 - 2 y = 15

Add 2 y to both sides:

{ (9 x) / 2 = 2 y + 15

3 x - y = 10

Multiply both sides by 2/9:

{x = (4 y) / 9 + 10/3

3 x - y = 10

Substitute x = (4 y) / 9 + 10/3 into the second equation:

{x = (4 y) / 9 + 10/3

3 ((4 y) / 9 + 10/3) - y = 10

3 ((4 y) / 9 + 10/3) - y = ((4 y) / 3 + 10) - y = y/3 + 10:

{x = (4 y) / 9 + 10/3

y/3 + 10 = 10

In the second equation, look to solve for y:

{x = (4 y) / 9 + 10/3

y/3 + 10 = 10

Subtract 10 from both sides:

{x = (4 y) / 9 + 10/3

y/3 = 0

Multiply both sides by 3:

{x = (4 y) / 9 + 10/3

y = 0

Substitute y = 0 into the first equation:

Answer: {x = 10/3, y = 0