Question

Graphically the pair of equations 7x-y=5;21x-3y=10 represent two lines which are??

Answer 1

EXPLANATION.

Graphically the pair of equations.

⇒ 7x - y = 5. - - - - - (1).

⇒ 21x - 3y = 10. - - - - - (2).

As we know that,

From equation (1), we get.

⇒ 7x - y = 5. - - - - - (1).

Put the values of x = 0 in the equation, we get.

⇒ 7(0) - y = 5.

⇒ - y = 5.

⇒ y = - 5.

Their Co-ordinates = (0,-5).

Put the values of y = 0 in the equation, we get.

⇒ 7x - (0) = 5.

⇒ 7x = 5.

⇒ x = 5/7.

⇒ x = 0.71.

Their Co-ordinates = (0.71,0).

From equation (2), we get.

⇒ 21x - 3y = 10. - - - - - (2).

Put the values of x = 0 in the equation, we get.

⇒ 21(0) - 3y = 10.

⇒ - 3y = 10.

⇒ y = - 10/3.

⇒ y = - 3.33.

Their Co-ordinates = (0,-3.33).

Put the values of y = 0 in the equation, we get.

⇒ 21x - 3(0) = 10.

⇒ 21x = 10.

⇒ x = 10/21.

⇒ x = 0.476.

Their Co-ordinates = (0.476,0).

Both curves are parallel to each other and never intersects each other.

Answer 2

GIVEN :

The pair of equations are 7x-y=5 and 21x-3y=10

TO FIND :

Graphically, the pair of equations 7x-y=5 and 21x-3y=10 represents which two lines

Given pair of equations:

$\sf \: 7x-y=5 \: --(1)$

$\sf \: If \: x = 0 \:then \: y = -5$

$\sf \: If \:x = 1 \: then \: y = 2$

plotting the points A(0,-5) and B(1,2) on the graph and joining them we get a straight line.

$\sf \: 21x - 3y = 10 \:--(2)$

$\sf \: If \: x = \frac{1}{3} \:then \: y = -1$

then y=-1

$\sf \: If \: x = \frac{1}{21} \:then \: y = -3$

then Y=-3

plotting the points C and D on the graph and joining them we get a straight line.

From the graph ,we conclude that these two lines are "parallel. "