Question

What is the solution to the system of equations?

`6x-9y=16`

2x – 3y = 7

Answer 1

To solve the system of equations

1. \( 6x - 9y = 16 \)
2. \( 2x - 3y = 7 \),

let's first simplify and solve these equations step by step.

### Step 1: Simplify the first equation.

The first equation can be simplified by dividing all terms by 3:

\[
2x - 3y = \frac{16}{3}
\]

So now we have:

**Equation 1:**
\[
2x - 3y = \frac{16}{3} \quad \text{(1)}
\]

**Equation 2:**
\[
2x - 3y = 7 \quad \text{(2)}
\]

### Step 2: Compare the two equations.

From (1) and (2), we have:

\[
\frac{16}{3} = 7
\]

Since \(\frac{16}{3} = 5.33... \neq 7\), the two equations are inconsistent, meaning they represent parallel lines that do not intersect.

### Conclusion

The system of equations has **no solution** as the equations describe parallel lines.