https://file.aiquickdraw.com/mathbot/file/1729319408824ogzikjyw.jpg

The system of equations given in the image is:

\[
\begin{aligned}
1) & \quad 2x - 3 = y \\
2) & \quad x + 2y = -21
\end{aligned}
\]

We need to solve for \(x\) and \(y\) to find the solution.

### Step 1: Substitute \(y\) from the first equation into the second equation.

From equation 1, we have:

\[
y = 2x - 3
\]

Substitute this expression for \(y\) in the second equation:

\[
x + 2(2x - 3) = -21
\]

### Step 2: Simplify the equation.

\[
x + 4x - 6 = -21
\]

Combine like terms:

\[
5x - 6 = -21
\]

### Step 3: Solve for \(x\).

Add 6 to both sides:

\[
5x = -21 + 6 = -15
\]

Now divide by 5:

\[
x = \frac{-15}{5} = -3
\]

### Step 4: Solve for \(y\).

Substitute \(x = -3\) back into the first equation:

\[
y = 2(-3) - 3 = -6 - 3 = -9
\]

### Final Answer:
The solution to the system is \(x = -3\) and \(y = -9\), which corresponds to option **B**: \((-3, -9)\).

Would you like further details or have any questions?

### Related Questions:
1. How do you solve a system of equations using the substitution method?
2. What are other methods to solve a system of linear equations?
3. What happens if a system of equations has no solution?
4. How do you solve a system of equations graphically?
5. Can a system of linear equations have infinitely many solutions?

### Tip:
When solving systems of equations, always check if you can simplify one of the equations to isolate a variable easily. This makes substitution much simpler.

What is the solution (x, y) of the system of equations 2x - 3 = y and x + 2y = -21?

Learn how to solve a system of equations using the substitution method. In this problem, we solve for x and y in the equations 2x - 3 = y and x + 2y = -21. Follow the step-by-step solution, suitable for students in Grades 7-9.

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