Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this.

-7x Ð 5y = 1.5

-5x Ð 4y = 4.5

To solve this system of equations using the elimination method, we need to manipulate one or both equations so that when combined, one of the variables will be eliminated.

Let's start by multiplying both sides of the first equation by -4 and the second equation by -5 to make the coefficients of x in both equations the same:

-4 * (-7x) - 4 * 5y = -4 * 1.5
-5 * (-5x) - 5 * (-4y) = -5 * 4.5

This simplifies to:

28x + 20y = -6
25x + 20y = -22.5

Next, subtract the second equation from the first equation:

(28x + 20y) - (25x + 20y) = -6 - (-22.5)

This simplifies to:

3x = 16.5

Now, divide both sides of the equation by 3:

3x/3 = 16.5/3

This gives us:

x = 5.5

Substitute the value of x back into one of the original equations. Let's use the first equation:

-7x - 5y = 1.5
-7(5.5) - 5y = 1.5

This simplifies to:

-38.5 - 5y = 1.5

Next, subtract 1.5 from both sides:

-38.5 - 5y - 1.5 = 1.5 - 1.5

This simplifies to:

-40 - 5y = 0

Now, add 40 to both sides:

-40 - 5y + 40 = 0 + 40

This simplifies to:

-5y = 40

Finally, divide both sides by -5:

-5y / -5 = 40 / -5

This gives us:

y = -8

Therefore, the solution to the system of equations is x = 5.5 and y = -8.

There is no infinite number of solutions or no solution for this system.