Gaige's error occurred during the isolation of the term with y. The correct result for y is -1, suggesting a mistake in the sign or calculation during the substitution process.
Gaige's first step is to substitute the expression for x from the second equation (-4x - 15y = -17) into the first equation (x = 5y + 13). Let's examine this substitution process:
The second equation is x = 5y + 13. Now, substitute this expression for x into the first equation:
-4(5y + 13) - 15y = -17
Now, distribute the -4 on the left side:
-20y - 52 - 15y = -17
Combine like terms:
-35y - 52 = -17
Next, isolate the term with y by adding 52 to both sides:
-35y = 35
Finally, divide both sides by -35 to solve for y:
y = -1
So, it seems Gaige made an error in the process. The correct result for y should be -1, but further examination is needed to identify the specific step where the error occurred. The error could be related to a sign mistake or a miscalculation during the substitution process.