Question
\( y=2 x-1 \) \( 5 x-4 y=1 \) Is \( (1,1) \) a solution of the system? Choose 1 answeri (A) Yes (B) No
Ask by Ayala Rogers. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( (1,1) \) is a solution to the system.
Solution
**(A) Yes**
**Explanation:**
Let's verify if the point \((1, 1)\) satisfies both equations in the system.
1. **First equation:** \( y = 2x - 1 \)
\[
1 = 2(1) - 1 \\
1 = 2 - 1 \\
1 = 1 \quad \text{(True)}
\]
2. **Second equation:** \( 5x - 4y = 1 \)
\[
5(1) - 4(1) = 1 \\
5 - 4 = 1 \\
1 = 1 \quad \text{(True)}
\]
Since \((1, 1)\) satisfies both equations, it is indeed a solution to the system.
Reviewed and approved by the UpStudy tutoring team
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Extra Insights
To check if \( (1,1) \) is a solution of the system, we substitute \( x = 1 \) and \( y = 1 \) into both equations. For the first equation \( y = 2x - 1 \): Substituting gives \( 1 = 2(1) - 1 \) which simplifies to \( 1 = 1 \) (True). For the second equation \( 5x - 4y = 1 \): Substituting gives \( 5(1) - 4(1) = 1 \) which simplifies to \( 5 - 4 = 1 \) (True). Since both equations are satisfied, the answer is (A) Yes.