The image contains a system of linear equations with a solution being found using the substitution method. Let me transcribe and verify the solution provided.

System of equations:

1. $x = -3y + 16$
2. $2x + 5y = 14$

Substitution method:

From the first equation, $x = -3y + 16$, substitute $x$ into the second equation.

$2(-3y + 16) + 5y = 14$

Simplify: $-6y + 32 + 5y = 14$

Combine like terms: $-y + 32 = 14$

Solve for $y$: $-y = 14 - 32$ $-y = -18$ $y = 18$

Now substitute $y = 18$ back into the first equation to find $x$: $x = -3(18) + 16$ $x = -54 + 16$ $x = -38$

Solution:

The solution to the system of equations is: $x = -38, \, y = 18$

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Related Questions:

1. How is substitution used in solving systems of equations?
2. What are alternative methods for solving systems of equations (e.g., elimination)?
3. How can we verify solutions to systems of equations?
4. What types of systems of equations have no solution or infinite solutions?
5. How do graphing methods compare to algebraic methods for solving equations?

Tip: Always substitute your solution back into both equations to ensure accuracy.