What is the solution to the system of equations y = 3x + 7 and y = x + 9?

To solve the system of equations y = 3x + 7 and y = x + 9, we will set the two equations equal to each other since both are equal to y.

Thus, we can write:

3x + 7 = x + 9

Next, we’ll isolate the variable x. Start by subtracting x from both sides:

3x - x + 7 = 9

This simplifies to:

2x + 7 = 9

Now, subtract 7 from both sides:

2x = 9 - 7

Which gives us:

2x = 2

Now, divide both sides by 2 to find x:

x = 1

Now that we have the value of x, we can substitute it back into one of the original equations to find y. Let’s use the second equation:

y = x + 9

Substituting x = 1 gives us:

y = 1 + 9

So, y = 10.

Therefore, the solution to the system of equations is:

(x, y) = (1, 10)

In conclusion, the solution to the system of equations y = 3x + 7 and y = x + 9 is (1, 10).