Question

the equation x+2y=3 and 2x+4y+7=0 represents the pair of ............. lines​

Answer 1

Step-by-step explanation:

Given equation x+ 2y = 3

then, x+ 2y-3 = 0

also 2x +4y +7=0

Now a1=1; b1 = 2; c1=-3

also, a2=2; b2=4 and c2 = 7

so, a1/a2=1/2; b1/ b2=1/4=1/2;c1/c2=-3/3= -1

here a1/ a2= b1/ b2 is not equal to c1/ c2

so here the condition of unique solution arise and we know that in unique solution there is parallel lines.So the equation represents parallel line

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Answer 2

The equations represent a pair of parallel lines.  

Given,

x+2y=3 and 2x+4y+7=0

To Find,

The equations represent a pair of what lines?

Solution,

We can solve the question as follows:

It is asked that we have to find the pair of lines the given equations represent. The equations are:

$x + 2y = 3$

$2x + 4y + 7 = 0$

The equations are of the form:

$a_{1} x + b_{1} x + c_{1} = 0$ and $a_{2} x + b_{2} x + c_{2} = 0$

If $\frac{a_{1} }{a_{2} } = \frac{b_{1} }{b_{2} }$, the lines intersect.

If $\frac{a_{1} }{a_{2} } = \frac{b_{1} }{b_{2} } = \frac{c_{1} }{c_{2} }$, the lines coincide.

If $\frac{a_{1} }{a_{2} } = \frac{b_{1} }{b_{2} } \neq \frac{c_{1} }{c_{2} }$, the lines are parallel.

From the given equations,

$a_{1} = 1, b_{1} = 2, c_{1} = -3$ and $a_{2} = 2, b_{2} = 4, c_{2} = 7$

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

$\frac{b_{1} }{b_{2} } = \frac{2 }{4 }= \frac{1 }{2 },$

$\frac{c_{1} }{c_{2} }= \frac{-3 }{7 }$

Therefore,

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

Hence, the lines are parallel.

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