5x – 9y = 7, 7y – 3x = -5

I don't see a question here.

no, but I think we can assume that he wants the solution to the system of equations. Michael, you really should ask a question, and not just dump problems into the forum. Also, show where you get stuck. If you truly have no clue, then you cannot have read the material; a problem would not have been posed for completely new material.

So, using your favorite method, you will arrive at the solution

x = 1/2
y = -1/2

To solve this system of equations, you can use different methods such as elimination, substitution, or graphing. I will use the elimination method to explain.

Step 1: Multiply the two equations by appropriate numbers to eliminate a variable. Here, we can multiply the first equation by 7 and the second equation by 5 to make the coefficient of "y" in both equations the same.

7(5x - 9y) = 7(7)
5(7y - 3x) = 5(-5)

This simplifies the equations to:

35x - 63y = 49
35y - 15x = -25

Step 2: Now, we can add the two equations together to eliminate the variable "x".

(35x - 63y) + (35y - 15x) = 49 + (-25)

This simplifies to:

35x - 15x - 63y + 35y = 24

Combine like terms:

20x - 28y = 24

Step 3: Now we have another equation with only one variable left. We can solve for "x" in terms of "y" or "y" in terms of "x".

Let's solve for "y" in terms of "x".

20x - 28y = 24

Rearrange the equation:

-28y = -20x + 24

Divide both sides by -28 to solve for "y":

y = (20/28)x - (24/28)

Simplify:

y = (5/7)x - (3/7)

So the solution to the system of equations is y = (5/7)x - (3/7).