x and y are variables. That means they represent numbers that are unknown. When we solve for x or y, we are trying to find what number the variable represents.

Y is a number that equals both 5x-9 and 3x+7. If it is a number, it can only have one value, so we can say that 5x-9 and 3x+7 have the same value.

In other words, 5x-9 = 3x+7.

Another way of thinking about this step is substitution. y=3x+7, so in the equation y=5x-9, we can replace the y with 3x+7. It will give 3x+7 = 5x-9.

In either case, we have this new equation

5x-9 = 3x+7.

From here it's just simple algebra- subtract 3x from each side

2x -9 = 7

and add 9 to each side

2x = 16

and divide each side by 2.

x = 8.

All these steps work because if two things equal each other, when you do the same thing to both of them (such as add 9), the new values will still equal each other.

Now that we know that x = 8, we can take one of the original equations

y=5x-9

and put 8 in for x.

y=5*(8) -9.

If x represents the value 8, we can obviously switch out x for 8.

Now simplify

y=40 -9

y = 31

Now we know that x = 8 and y = 31.

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