Question

Show that the pair of equations 2y=4x-6, 2x=y+3 has infinite solutions

Answer 1

Answer:

Step-by-step explanation:

for equation 1:

2y=4x-6

=> 4x-2y-6=0

here, a1 = 4 , b1 = -2, c1 = -6

for equation2:

2x=y+3

=>2x-y-3=0

here a2 = 2, b2 = -1, c2 = -3

a1/a2      b1/b2        c1/c2

=4/2         -2/-1         -6/-3

= 2                2             2

as a1/a2=b1/b2=c1/c2

the equations have infinite solutions.

Answer 2

The given system of equation can be written as :

4x - 2y - 6 = 0

2x - y - 3 = 0

The given equations are of the form

$a_{1}x + b_{1}y + c_{1} = 0$

$a_{2}x + b_{2}y + c_{2} = 0$

Where,

$a_{1} = 4 \: \: \: \: \: \: \: b_{1} = 2 \: \: \: \: \: \: \: \: c_{1} = - 6 \\ a_{2} = 2 \: \: \: \: \: \: \: b_{2} = - 1 \: \: \: \: c_{2} = - 3$

Now,

$\frac{a_{1}}{a_{2}} = \frac{4}{2} = 2 \\ \\ \frac{b _{1}}{b_{2}} = \frac{ - 2}{ - 1} = 2 \\ \\ \frac{c_{1}}{c_{2}} = \frac{ - 6}{ - 3} = 2$

$\sf{Clearly} ( \frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}} ) \: so \: the \: given \: system \: of \: equations\: has \: infinitely \: many \: solutions$