Solve the following system of equations: x + 2y = 14, x + 3y = 9

To solve the system of equations:

• x + 2y = 14
• x + 3y = 9

We can use either the substitution method or the elimination method. Here, I will use the elimination method for clarity.

First, let’s express both equations:

1. Equation 1: x + 2y = 14
2. Equation 2: x + 3y = 9

Next, we’ll eliminate x by subtracting the first equation from the second equation:

x + 3y - (x + 2y) = 9 - 14

This simplifies to:

y = -5

Now that we have the value of y, we can substitute it back into either of the original equations to find x. Let’s use Equation 1:

x + 2(-5) = 14

This simplifies to:

x - 10 = 14

Now, solving for x:

x = 14 + 10

x = 24

Thus, the solution to the system of equations is:

x = 24, y = -5

In conclusion, the pair of values (24, -5) satisfies both original equations, which confirms our solution is correct.