Pair of Linear Equations in Two Variables - Class 10 CBSE

How many solutions does the pair of equations y = 0 and y = -5 have, and what is the shape of lines represented? (2013)

If  $ax+by=a^2-b^2$ and  $bx+ay=0$ , find the value of  $\left(x+y\right)$ . (2013)

For what value of k, the pair of equations 4x – 3y = 9, 2x + ky = 11 has no solution? (2017D)

Calculate the area bounded by the line x + y = 10 and both the co-ordinate axes. (2012)

Solve for x and y:  $\frac{10}{x+y}+\frac{2}{x-y}=4$    and 
 $\frac{15}{x+y}-\frac{5}{x-y}=-2$  ;       x + y ≠ 0  ,   x – y ≠ 0 (2012, 2017D)

Solve the following pair of linear equations for x and y:

141x + 93y = 189 ;

93x + 141y = 45 (2013)

Find the value of  $\alpha$  and  $\beta$  for which the following pair of linear equations has infinite number of solutions:
 $2x+3y=7$  ;
 $\alpha x+\left(\alpha+\beta\right)y=28$   (2013)

A man earns ₹ 600 per month more than his wife. One-tenth of the man’s salary and  $\frac{1}{6}$ th of the wife’s salary amount to ₹ 1,500, which is saved every month. Find their incomes. (2014)

Sita Devi wants to make a rectangular pond on the road side for the purpose of providing drinking water for street animals. The area of the pond will be decreased by 3 square feet if its length is decreased by 2 ft. and breadth is increased by 1 ft. Its area will be increased by 4 square feet if the length is increased by 1 ft. and breadth remains same. Find the dimensions of the pond. (2014)

Speed of a boat in still water is 15 km/h. It goes 30 km upstream and returns back at the same point in 4 hours 30 minutes. Find the speed of the stream. (2017D)

A man travels 300 km partly by train and partly by car. He takes 4 hours if the travels 60 km by train and the rest by car. If he travels 100 km by train and the remaining by car, he takes 10 minutes longer. Find the speeds of the train and the car separately. (2017D)