Which statement is correct about the graph of the equations (22x+33y=99) and (2x+3y=12)?

Correct answer: Lines are distinct parallel

For two linear equations, compare the ratios of the coefficients of x and y with the ratio of the constant terms. If the x-coefficient ratio and y-coefficient ratio are equal, but the constant ratio is different, the two equations represent different parallel lines. Such lines never meet, so the pair has no common solution. This is the idea behind option C, distinct parallel lines.

Here, the ratios are \(22/2=11\) and \(33/3=11\), while \(99/12=8.25\). Thus the first two ratios are equal, but the third is not. Therefore, the lines have the same direction but different positions. They are not coincident, because coincident lines would have all three ratios equal; they are also not perpendicular or intersecting.