A linear equation in two variables has :
A. Unique solutions
B. No solutions
C. Infinitely many solutions
D. Graphical solutions
E. None of these
Choose the correct answer from the options given below :
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → C
A linear equation in two variables, \(ax+by+c=0\) (with \(a\) and \(b\) not both zero), has a straight line as its graph, and every point on that line is a solution. For any value of one variable, the other can be worked out, so there is no end to the solutions.
A. Unique solutions Incorrect. One equation cannot fix both \(x\) and \(y\): \(x+y=5\) is met by (0, 5), (1, 4), (2, 3) and many more. A unique solution needs a second equation whose line cuts the first.
B. No solutions Incorrect. “No solution” describes two parallel lines, a pair of equations; a single equation always has solutions.
C. Infinitely many solutions Correct. Every point on its line is a solution, so it has infinitely many.
D. Graphical solutions Incorrect. “Graphical” names a method of finding solutions (drawing the lines), not a kind or number of solutions that an equation has.
E. None of these Incorrect. C is true, so “none of these” cannot be.