Question

Ax+6y=18\\ x + 3y =4.5a

Answer 1

1) ax=18-6y
x=18-6y/a, a≠0
2) x+3y-3y=4,5a-3y
x=4,5a-3y

Answer 2

To solve the system of equations:

1. Ax + 6y = 18
2. x + 3y = 4.5a

We can use the method of substitution or elimination. I'll use the method of substitution here:

From equation 2), we can solve for x: x = 4.5a - 3y

Substituting this value of x into equation 1), we get: A(4.5a - 3y) + 6y = 18

Expanding the equation: 4.5aA - 3Ay + 6y = 18

Rearranging the terms: (4.5aA - 3Ay) + 6y = 18

Combining like terms: (4.5aA - 3A)y + 6y = 18

Factor out y: (4.5aA - 3A + 6)y = 18

Divide both sides by (4.5aA - 3A + 6): y = 18 / (4.5aA - 3A + 6)

Now that we have the value of y, we can substitute it back into equation 2) to find x: x + 3y = 4.5a

Substituting the value of y we found: x + 3(18 / (4.5aA - 3A + 6)) = 4.5a

Multiplying through by (4.5aA - 3A + 6): x(4.5aA - 3A + 6) + 54 = 4.5a(4.5aA - 3A + 6)

Expanding the equation: 4.5aAx - 3Ax + 6x + 54 = 20.25a^2A - 13.5aA + 27a + 27

Rearranging the terms: 4.5aAx - 3Ax + 6x - 20.25a^2A + 13.5aA - 27a = 27 - 54

Combining like terms: (4.5aA - 3A + 6)x - (20.25a^2A - 13.5aA + 27a) = -27

Divide both sides by (4.5aA - 3A + 6): x = (-27) / (4.5aA - 3A + 6)

So the solution to the system of equations is: x = (-27) / (4.5aA - 3A + 6) y = 18 / (4.5aA - 3A + 6)