linear equation

Solve the following pair of linear equations:
y -4x= 1
6x- 5y= 9

• x=-1

  y=-1

• x=-1

  y=-3

Find whether the lines representing the following pair of linear equations intersect at a point, are parallel or coincident: 2x – 3y + 6 = 0,4x – 5y + 2 = 0

4 chairs and 3 tables cost ? 2100 and 5 chairs and 2 tables cost ? 1750. Find the cost of one chair and one table separately

• chair=100

  table=500

• chair=150

  table=500

Solve for x and y:

6(ax + by) = 3a + 2b
6(bx – ay) = 3b -2a

• x=1/2

  y=1/3

• x=1/2

  y=1/2

In a two digit number, the digit in the unit place is twice of the digit in the tenth place. If the digits are reversed, the new number is 27 more than the given number. Find the number.

The area of a rectangle reduces by 160 m if its length is increased by 5 m and breadth is reduced by 4 m. However, if length is decreased by 10 m and breadth is increased by 2 m, then its area is decreased by 100 m2. Find the dimensions of the rectangle.

• l=60

  b=20

• l=20

  b=60

Places A and B are 100 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 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?

Answer explanation

x=60

y=40

At a certain time in a zoo, the number of heads and the number of legs of tiger and peacocks were counted and it was found that there were 47 heads and 152 legs. Find the number of tigers and peacocks in the zoo

• tiger=29

  peacock=18

• tiger=22

  peacock=12

For what values of p and q will the following pair of linear equations has infinitely many solutions?
4x + 5y = 2;
(2p + 7q)x + (p + 8q)y = 2q-p + 1

• p=-1

  q=2

• p=3

  q=-4

Solve the following pair of equations for x and y

• x=a

  y=b

• x=b

  y=-a