CBSE Guess > Papers > Question Papers > Class X > 2009 > Mathematics > Mathematics

Q. 17. Check graphically whether the pair of equations 3x + 5y = 15 and x – y = 5 is consistent. Also find the coordinates of the points where the graphs of the equations meet the y-axis.

Sol .

By plotting the points and joining them, the lines intersect at A(5, 0)
x = 5, y = 0
The pair of given equation is consistent.
The equation 3x + 5y = 15 meets the y-axis at
B(0, 3)The equation x – y = 5 meets the y-axis at C(0, – 5)

Or

Places A and B are 160 km apart on a highway. One car starts from A and another from B at the
same time. If the cars travel in the same direction at different speeds, they meet in 8 hours, but if
they travel towards each other, they meet in 2 hours. What are the speeds of the two cars?

Sol .

Let the speed of 1st car starting from place A = x km/hr
and the speed of 2nd car starting from place B = y km/hr
When two cars travel in the same direction
Distance covered by 1st car in 8 hours
= 160 km + Distance covered by 2nd car
8x = 8y + 160 …( Q Distance = Speed time)
x = y + 20 …(i) (Dividing both sides by 8)
When two cars travel towards each other
2x + 2y = 160 …( D = ST)
x + y = 80 …(Dividing both sides by 2)
y + 20 + y = 80 …[From (i)]
2y = 80 – 20 = 60

From (i), x = 30 + 20 = 50
Speed of car starting from place A = 50 km/hr
and speed of car starting from place B = 30 km/hr.

Mathematics 2009 Question Papers Class X
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