Question

what is the solution of (7/2)x-(9/2)=2y and 4y=7x-9?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the solution for the system of equations, we can use the method of substitution.

First, let's solve the second equation for y:

4y = 7x - 9
y = (7x - 9)/4

Now, we can substitute this expression for y into the first equation:

(7/2)x - (9/2) = 2((7x - 9)/4)

Multiplying through by 4 to eliminate the fraction:

14x - 18 = 2(7x - 9)

Expanding and simplifying:

14x - 18 = 14x - 18

We can see that the variable x cancels out, which means there are infinitely many solutions for this system of equations. This indicates that the equations represent the same line in a two-dimensional coordinate system.

Therefore, the solution to the system is any point on the line represented by the equations.