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: See what each equation is telling us.
We have $2x - 5y = 7$ and $y - 1 = 0$. The second one is the easier of the two, it simply fixes the value of $y$ for us.
Step 2: Pin down y, then find x.
From the second equation, \[ y = 1 \] Put this into the first equation: \[ 2x - 5(1) = 7 \] \[ 2x = 12 \] \[ x = 6 \]
Step 3: Write the point and match it.
So the point common to both lines is $(6, 1)$, and since a y-coordinate of 1 combined with this x-value is the only pair that satisfies both equations together, this is the required solution. \[ \boxed{(6,\ 1)} \]