Question

Which of these describes the system of linear equations below?

3x-2y=7
6x-4y=14

a) the system has no solutions.
b) the system has infinitely many solutions.
c) the ration of the-coordinate to the y-coordinate of the only solution is 2 : 1.
d) the difference between the x-coordinate and y-coordinate of the only solution is one.

Answer 1

Given:

The system of equations is

`3x-2y=7`

`6x-4y=14`

To find:

The correct statement for the given system of equations.

Solution:

On comparing the given equations and general form of linear equation, i.e.,
`ax+by+c=0`, we get

`a_1=3,b_1=-2,c_1=-7`

`a_2=6,b_2=-4,c_2=-14`

Here,

`(a_1)/(a_2)=(3)/(6)=(1)/(2)`

`(b_1)/(b_2)=(-2)/(-4)=(1)/(2)`

`(c_1)/(c_2)=(-7)/(-14)=(1)/(2)`

Since,
`(a_1)/(a_2)=(b_1)/(b_2)=(c_1)/(c_2)`, therefore, the two equations are equivalent and the system has infinitely many solutions.

Hence, the correct option is b.