10 Question MCQ (including Assertion)

The pair of equations \(x=a\) and \(y=b\) graphically represents lines which are:

A shopkeeper is making gift baskets with apples ( \(a\) ) and oranges ( \(o\) ). One basket type follows the rule \(a=20\). Another follows \(3 a+4 o=100\). If he wants to create a basket that satisfies both rules, what does he need to find?

Equation of another line parallel to the line represented by \(2 x-6 y=7\) is :

A boat's speed in still water is \(x \mathrm{~km} / \mathrm{h}\), and the speed of the stream is \(y \mathrm{~km} / \mathrm{h}\). Its speed upstream is given by \(x-y=5\) and downstream by \(x+y=15\). What does the value of \(x\) represent?

Assertion (A): The area of the trapezium formed by the lines \(3 x+4 y-12=\) 0 and \(3 x+4 y=6\) is \(\frac{9}{2}\) square units.
Reason (R): The system of equations \(a_1 x+b_1 y+c_1=0\) and \(a_2 x+b_2 y+ c_2=0\) is inconsistent, if \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\).

The equations \(y=x+2\) and \(y=-x+4\) represent the paths of two hikers on a map. Which of the following descriptions best represents the graph of their paths?

A system of linear equations is called 'inconsistent'. In a real-world context, what does this imply?

The pair of equations \(5 x-15 y=8\) and \(3 x-9 y=\frac{24}{5}\) has

A graph represents the distance ( \(y\)-axis, in km ) versus time ( \(x\)-axis, in hours) for two cyclists, \(A\) and \(B\). The path of Cyclist \(A\) is a line starting from the origin \((0,0)\). The path of Cyclist \(B\) is a line starting from \((0,10)\), indicating a 10 km head start. The line for Cyclist \(A\) is steeper than the line for Cyclist B, and they intersect at a point. What can be concluded at the point of intersection?