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

-5x – 7y = 25.5
-2x + 10y = -9

To solve the given system of equations using the elimination method, follow these steps:

Step 1: Multiply the equations by appropriate numbers to make the coefficients of one of the variables (x or y) the same or additive inverses.

In this case, let's make the coefficient of y in both equations the same. To achieve this, multiply the first equation by 10 and the second equation by 7:

-5x * 10 - 7y * 10 = 25.5 * 10
-2x * 7 + 10y * 7 = -9 * 7

This simplifies the equations to:
-50x - 70y = 255
-14x + 70y = -63

Step 2: Add the two resulting equations.

Combine the equations by adding them vertically:

(-50x - 70y) + (-14x + 70y) = 255 + (-63)

This simplifies to:
-64x = 192

Step 3: Solve for x.

Divide both sides of the equation by -64:
x = -192 / -64
x = 3

Step 4: Substitute the value of x into one of the original equations to solve for y.

Let's choose the first equation:
-5x – 7y = 25.5

Substitute x = 3:
-5(3) – 7y = 25.5
-15 - 7y = 25.5

Step 5: Solve for y.

Add 15 to both sides of the equation:
-7y = 25.5 + 15
-7y = 40.5

Divide both sides of the equation by -7:
y = 40.5 / -7
y = -5.7857 (rounded to four decimal places)

Therefore, the solution to the system of equations is x = 3 and y ≈ -5.7857.

The plan is to get the coefficients of either the x's or the y's to be the same or opposite

I will go for the x's to be the same ...
1st equation times (-2) : --> 10x + 14y = -51
2nd equation times (-5): --> 10x - 50y = 45
subtract them ....
64y = -96
y = -96/64 = -3/2

sub into original 2nd
-2x + 10(-3/2) = -9
-2x = -9 + 15 = 6
x = -3