https://file.aiquickdraw.com/mathbot/file/1726310984131s5itw1u3.jpg

The system of linear equations provided in the image is:

\[
\begin{aligned}
1. & \quad x - 2y = 21 \\
2. & \quad 4x - 5y = 54
\end{aligned}
\]

We can solve this system using the substitution or elimination method. I will use the substitution method here.

### Step 1: Solve the first equation for \(x\):
\[
x = 2y + 21
\]

### Step 2: Substitute \(x = 2y + 21\) into the second equation:
\[
4(2y + 21) - 5y = 54
\]

### Step 3: Expand and simplify the equation:
\[
8y + 84 - 5y = 54
\]
\[
3y + 84 = 54
\]
\[
3y = 54 - 84
\]
\[
3y = -30
\]
\[
y = -10
\]

### Step 4: Substitute \(y = -10\) back into \(x = 2y + 21\) to find \(x\):
\[
x = 2(-10) + 21
\]
\[
x = -20 + 21
\]
\[
x = 1
\]

### Solution:
\[
(x, y) = (1, -10)
\]

Would you like a detailed breakdown of any steps? Here are some related questions:

1. What are the different methods to solve a system of linear equations?
2. How can the elimination method be applied to this system?
3. What does it mean for a system of equations to be inconsistent or dependent?
4. How do you solve systems of equations using matrices?
5. Can graphical methods be used to solve systems of equations? If so, how?

**Tip:** Always double-check your solution by substituting the values of \(x\) and \(y\) back into both original equations.

Solve the system of equations: x - 2y = 21 and 4x - 5y = 54.

Learn how to solve the system of linear equations x - 2y = 21 and 4x - 5y = 54 using the substitution method. This problem covers algebraic concepts suitable for students in Grades 8-10.

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