107
(a) Solve graphically the following pair of linear equations :
$2x - y = 2$ and $4x - y = 4$
Also, write the coordinates of the points where the lines represented by these equations cut the y-axis.
OR
(b) An academy offering cricket coaching bought $10$ bats and $5$ balls for ₹32,500. Later, the academy bought $2$ bats and $8$ balls for ₹10,000. If there is no change in the cost of the bat and of the ball, find the cost of $1$ bat and $1$ ball.
$2x - y = 2$ and $4x - y = 4$
Also, write the coordinates of the points where the lines represented by these equations cut the y-axis.
OR
(b) An academy offering cricket coaching bought $10$ bats and $5$ balls for ₹32,500. Later, the academy bought $2$ bats and $8$ balls for ₹10,000. If there is no change in the cost of the bat and of the ball, find the cost of $1$ bat and $1$ ball.
Show SolutionHide Solution↓
Solution: (a) Correct graph of each equation [1+1 marks]
Solution is $x=1, y=0$ or $(1, 0)$ [1/2 mark]
Lines cut y axis at $(0, -2)$ and $(0, -4)$ [1/2 mark]
OR
(b) Let the cost of $1$ bat be $\text{Rs}x$ and the cost of $1$ ball be $\text{Rs}y$
A.T.Q.
$10x + 5y = 32500$ or $2x + y = 6500$ -------(i) [1 mark]
$2x + 8y = 10000$ or $2x + 8y = 10000$ ----(ii) [1 mark]
Solving (i) and (ii) to get $x = 3000$ and $y = 500$ [1/2 + 1/2 mark]
Cost of $1$ bat = ₹3,000
Cost of $1$ ball = ₹500
Solution is $x=1, y=0$ or $(1, 0)$ [1/2 mark]
Lines cut y axis at $(0, -2)$ and $(0, -4)$ [1/2 mark]
OR
(b) Let the cost of $1$ bat be $\text{Rs}x$ and the cost of $1$ ball be $\text{Rs}y$
A.T.Q.
$10x + 5y = 32500$ or $2x + y = 6500$ -------(i) [1 mark]
$2x + 8y = 10000$ or $2x + 8y = 10000$ ----(ii) [1 mark]
Solving (i) and (ii) to get $x = 3000$ and $y = 500$ [1/2 + 1/2 mark]
Cost of $1$ bat = ₹3,000
Cost of $1$ ball = ₹500