Kabir drew 2x − y = 2 (thick blue line) and 4x − 2y = 4 (dashed orange line) on the same grid. The two graphs lie exactly on top of each other, and points A, B, C are marked on them. Which statement is correct?

Question

Accepted Answer

The pair has infinitely many solutions: A, B, C and every other point of the line. The lines coincide, so every point on the line satisfies both equations, e.g. C(2, 2): 2(2) - 2 = 2 and 4(2) - 2(2) = 4. Coincident lines give infinitely many solutions (2/4 = -1/-2 = 2/4).

Kabir drew $2 x - y = 2$ (thick blue line) and $4 x - 2 y = 4$ (dashed orange line) on the same grid. The two graphs lie exactly on top of each other, and points A, B, C are marked on them. Which statement is correct?

Step-by-Step Solution

Key idea: Three geometric possibilities

Master this chapter in 30 minutes a day.

More Class 10 Pair of Linear Equations in Two Variables practice

Kabir drew 2x−y=2 (thick blue line) and 4x−2y=4 (dashed orange line) on the same grid. The two graphs lie exactly on top of each other, and points A, B, C are marked on them. Which statement is correct?

Step-by-Step Solution

Key idea: Three geometric possibilities

Master this chapter in 30 minutes a day.

More Class 10 Pair of Linear Equations in Two Variables practice

Kabir drew $2 x - y = 2$ (thick blue line) and $4 x - 2 y = 4$ (dashed orange line) on the same grid. The two graphs lie exactly on top of each other, and points A, B, C are marked on them. Which statement is correct?