Question
Monique is given the following problem. Her work is shown below. Describe and correct Monique's error.
Solve the following system: 2y - 3x = 8; y = 4x - 6
Monique
2y - 3x = 8; y = 4x - 6
4x - 6 - 3x = 8 x - 6 = 8 x = 14
y = 4(14) - 6 y = 56 - 6 y = 50
(14,50)
Make sure your answer is summarized and short and simple.
Solve the following system: 2y - 3x = 8; y = 4x - 6
Monique
2y - 3x = 8; y = 4x - 6
4x - 6 - 3x = 8 x - 6 = 8 x = 14
y = 4(14) - 6 y = 56 - 6 y = 50
(14,50)
Make sure your answer is summarized and short and simple.
Answers
GPT-4o mini
Monique's error occurs when she substitutes \( y \) into the first equation. She incorrectly combined the terms and simplified.
Instead of:
\[ 4x - 6 - 3x = 8 \]
She should have correctly substituted \( y \) from the second equation into the first:
\[ 2(4x - 6) - 3x = 8 \]
This simplifies to:
\[ 8x - 12 - 3x = 8 \]
Which further simplifies to:
\[ 5x - 12 = 8 \]
Then, adding 12 to both sides gives:
\[ 5x = 20 \]
Dividing by 5 results in:
\[ x = 4 \]
Now substitute \( x = 4 \) back into \( y = 4x - 6 \):
\[ y = 4(4) - 6 = 16 - 6 = 10 \]
The correct solution is \( (4, 10) \).
Instead of:
\[ 4x - 6 - 3x = 8 \]
She should have correctly substituted \( y \) from the second equation into the first:
\[ 2(4x - 6) - 3x = 8 \]
This simplifies to:
\[ 8x - 12 - 3x = 8 \]
Which further simplifies to:
\[ 5x - 12 = 8 \]
Then, adding 12 to both sides gives:
\[ 5x = 20 \]
Dividing by 5 results in:
\[ x = 4 \]
Now substitute \( x = 4 \) back into \( y = 4x - 6 \):
\[ y = 4(4) - 6 = 16 - 6 = 10 \]
The correct solution is \( (4, 10) \).