- AInfinitely many — every pair (7, y) works
- BExactly one, namely x=7
- CExactly two, one on each axis
- DNone, because y is missing
Step-by-Step Solution
x=7 is 1·x+0⋅y−7=0. Since y is multiplied by 0, any y at all works: (7, 0), (7, 1), (7, −5) … are all solutions. They form the vertical line x=7.
Answer: A) Infinitely many — every pair (7, y) works
Key idea: What does a 'solution' look like?
For an equation in TWO variables, a solution is a PAIR (x,y), not a single number.
Example: 2x+y=7. Try (1, 5): 2(1)+5=7 ✓. So (1, 5) is a solution.
Try (0, 7), (2, 3), (3, 1), (−1, 9) — all work. There are infinitely many. Two variables, one equation → one degree of freedom remaining.