Question

13 Graphically the pair of equations 5x - y + 6 = 0,
2x - 2/5y+ 7 = 0 represent two lines which are :
(a) intersecting and coincident
(b) intersecting at exactly two points
(c) coincident
(d) parallel
100 then value of​

Answer 1

given equations: 5x-y+6=0, 2x-2/5y+7=0

on solving 2nd equation, 5x-y+35/2=0

here the slopes of the 2 equations are same but different in the constant value

so these lines are parallel lines.

hope this helps you out.

Answer 2

Answer:

The line represent the pair of equation  5x - y + 6 = 0, 2x - 2/5y+ 7 = 0  are parallel

Explanation:

Given: The pair of equation are 5x - y + 6 = 0, 2x - 2/5y+ 7 = 0

To find: To find the pair of equation of two lines represents.

Solution

For two lines to be parallel then the equation will be

$\frac{a_{1} }{a_{2} } = \frac{b_{1} }{b_{2} } = \frac{c_{1} }{c_{2} }$

where,

⇒ a and b are coefficient of x and y.

⇒ c is a constant.

In the equation,

5x - y + 6 = 0,

$a_{1} = 5$

$b_{1}$ = -1

$c_{1}$  = 6

In the equation ,

$2x - \frac{2}{5} y + 7 = 0$

$a_{2}$ = 2

$b_{2}$ = $-\frac{2}{5}$

$c_{2}$ = 7

Substitute in the equation

⇒ $\frac{a_{1} }{a_{2} } = \frac{5}{2}$

⇒ $\frac{b_{1} }{b_{2} } = \frac{-1}{-\frac{2}{5} }$

⇒ $\frac{b_{1} }{b_{2} } = \frac{5}{2 }$

⇒ $\frac{c_{1} }{c_{2} } = \frac{6}{7}$

Therefore from the above solution coefficient of a is equal to coefficient of b

i.e

⇒ $\frac{a_{1} }{a_{2} } = \frac{b_{1} }{b_{2} }$ = $\frac{5}{2}$

This indicates the parallel lines

⇒ $\frac{a_{1} }{a_{2} } = \frac{b_{1} }{b_{2} } \neq \frac{c_{1} }{c_{2} }$

⇒ $\frac{5}{2} = \frac{5}{2} \neq \frac{6}{7}$

Final answer:

The lines represent by the given equation are parallel.

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