Question

Which is a solution to the system of equations?

x + 3y = 18
x + 2y = 14
Responses
A (6, 4)(6, 4)
B (4, 6)(4, 6)
C (6, -4)(6, -4)
D (-4, 6)(-4, 6)
E (-6, -4)

Answer 1

To find a solution to the system of equations:

1. \( x + 3y = 18 \)
2. \( x + 2y = 14 \)

We can solve the equations simultaneously. First, we can express one variable in terms of the other using either equation. Let's solve the second equation for \( x \):

\[
x = 14 - 2y
\]

Now, substitute this expression for \( x \) into the first equation:

\[
(14 - 2y) + 3y = 18
\]

This simplifies to:

\[
14 - 2y + 3y = 18
\]
\[
14 + y = 18
\]
\[
y = 18 - 14
\]
\[
y = 4
\]

Now that we have \( y = 4 \), we can substitute this value back into the equation we derived to find \( x \):

\[
x = 14 - 2(4)
\]
\[
x = 14 - 8
\]
\[
x = 6
\]

Thus, the solution to the system of equations is \( (6, 4) \).

Looking at the responses provided, the correct answer is:

**A (6, 4)**