Question

Which point is a solution to the system of linear equations?

y = −x + 6

x − 3y = 18?

Answer 1

To determine which point is a solution to the system of linear equations, we need to solve the equations simultaneously or check given points against both equations.

The system of equations is:

1. \( y = -x + 6 \)
2. \( x - 3y = 18 \)

**Step 1**: Substitute the expression for \( y \) from the first equation into the second equation.

Substituting \( y = -x + 6 \) into the second equation:

\[
x - 3(-x + 6) = 18
\]

**Step 2**: Simplify the second equation:

\[
x + 3x - 18 = 18
\]
\[
4x - 18 = 18
\]
\[
4x = 36
\]
\[
x = 9
\]

**Step 3**: Now, substitute \( x = 9 \) back into the first equation to find \( y \):

\[
y = -9 + 6 = -3
\]

So the solution to the system of equations is the point \( (9, -3) \).

**Verification**: Let's check if this point satisfies both equations.

For the first equation:
\[
y = -x + 6 \rightarrow -3 = -9 + 6 \quad \text{(true)}
\]

For the second equation:
\[
x - 3y = 18 \rightarrow 9 - 3(-3) = 18 \rightarrow 9 + 9 = 18 \quad \text{(true)}
\]

Thus, \( (9, -3) \) is indeed a solution to the system of equations. If you have specific points to check, please provide them, and I can verify which ones are solutions.