Question
Participation Activity \#4 This is similar to Try It \#6 in the OpenStax text. Solve the following system of equations in two variables. \[ 6 y-6 x=2 \] \( 6 y-6 x=6 \)
Ask by Cruz Ramos. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The system has no solution.
Solution
We are given two equations:
Equation 1: 6y – 6x = 2
Equation 2: 6y – 6x = 6
Notice that the left-hand sides of both equations are identical (6y – 6x). For the system to have a solution, the right-hand sides must also be equal. However, 2 ≠ 6.
Because the same expression cannot equal two different numbers at the same time, there is no pair (x, y) that can satisfy both equations simultaneously.
Answer: The system has no solution (it is inconsistent).
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Simplify this solution Beyond the Answer
To solve the system of equations: 1. The first equation can be simplified by dividing everything by 6: \( y - x = \frac{1}{3} \) (Equation 1). 2. Similarly, the second equation simplifies to: \( y - x = 1 \) (Equation 2). Now, we can see that both equations represent the same left side, but they equal different right sides. This indicates that the lines are parallel and will never intersect. Therefore, there is no solution for this system of equations.
