Question

Solution of the system of linear equations \(2x - 5y = 7\) and \(y - 1 = 0\) is :

• A. (6, 1)
• B. (0, 1)
• C. (1, -1)
• D. There is No solution

Hint:

Since \(y - 1 = 0 \implies y = 1\), the y-coordinate of the answer must be \(1\).
This immediately eliminates options (C) and (D).
Plugging \(x=6, y=1\) into \(2x - 5y\) yields \(12 - 5 = 7\), which matches option (A).

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
This question belongs to the topic of System of Linear Equations in Two Variables.
We are given two equations: a linear equation in two variables and a simple horizontal line equation.
Our objective is to find the unique point \((x, y)\) that satisfies both equations simultaneously.

Step 2: Key Formula or Approach:
We can use the substitution method.
The second equation gives the value of \(y\) directly.
By substituting this value into the first equation, we can determine the corresponding value of \(x\).

Step 3: Detailed Explanation:
Given equations:
Equation 1: \[ 2x - 5y = 7 \]
Equation 2: \[ y - 1 = 0 \]
From Equation 2, we directly get the value of \(y\):
\[ y = 1 \]
Substitute \(y = 1\) into Equation 1:
\[ 2x - 5(1) = 7 \]
\[ 2x - 5 = 7 \]
Add 5 to both sides:
\[ 2x = 7 + 5 \]
\[ 2x = 12 \]
Divide by 2:
\[ x = 6 \]
Thus, the solution is the coordinates \((6, 1)\).

Step 4: Final Answer:
The solution to the system of linear equations is \((6, 1)\).