Which method would be the simplest way to solve the system 7x + 5y = 19 and 7x + 2y = 16?

The simplest way to solve the system of equations 7x + 5y = 19 and 7x + 2y = 16 is to use the elimination method.

First, we can align both equations:

1. 7x + 5y = 19

2. 7x + 2y = 16

Next, we can subtract the second equation from the first:

(7x + 5y) – (7x + 2y) = 19 – 16

This simplifies to:

3y = 3

Now, dividing both sides by 3 gives us:

y = 1

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

7x + 2(1) = 16

This simplifies to:

7x + 2 = 16

Subtracting 2 from both sides gives us:

7x = 14

Finally, dividing both sides by 7 results in:

x = 2

So, the solution to the system of equations is:

x = 2, y = 1.