Corrected Options
(A)y = –4x + 5
(B)y = 4x – 5
(C)2y = 8x – 10
(D)–2y = –8x – 10
Answer:
(A)y = –4x + 5
Explanation:
A system of linear equations has one solution when the graphs of the two equations intersect at a point.
Given our first equation:
4x-y=5 which is the same as y=4x-5
- In Option B, the line is exactly the same line, therefore the system of equation will have infinite solutions.
- In Option C, 2y=8x-10 is equivalent to y=4x-5, likewise yielding infinite solutions like Option B.
- In option D, –2y = –8x – 10 is equivalent to y=4x+5. This pair will yield no solution.
Consider Option A: y = –4x + 5
Solving y = –4x + 5 and y=4x-5
–4x + 5=4x-5
-8x=-10
x=1.25
y=–4(1.25) + 5 =0
x=1.25, y=0
Thus option A is the only equation which could be the other equation