Question

HELP!! ASAP!!!!! Which system of equations below has infinitely many solutions?

a) y = –3x + 4 and y = –3x – 4
b) y = –3x + 4 and 3y = –9x + 12
c) y = –3x + 4 and y = -1/3+ 4
d) y = –3x + 4 and y = –6x + 8

Answer 1

Hello,

Answer B since
(y=-3x+4)* 3==> 3y=-9x+12 which is the second equation ==>infinity many solutions.

Answer 2

The correct option is B.
`y=-3x+4 \ \text{and}\ \ 3y=-9x+12`

Step-by-step explanation:

Consider the two linear equation:

`a_1x+b_1y+c_1=0\ \text{and}\ \ a_2x+b_2y+c_2=0`

The pair of linear equation has infinitely many solutions when:

`(a_1)/(a_2)=(b_1)/(b_2)=(c_1)/(c_2)`

Now consider the option.

Option a)
`y=-3x+4 \ \text{and}\ \ y=-3x-4`

The above equation can be written as:

`y+3x-4=0 \ \text{and}\ \ y+3x+4=0`

Therefore,

`(1)/(1)=(3)/(3)\\eq(-4)/(4)`

Thus, this pair has no solution.

Now consider the option B.
`y=-3x+4 \ \text{and}\ \ 3y=-9x+12`

The above equation can be written as:

`y+3x-4=0 \ \text{and}\ \ 3y+9x-12=0`

Therefore,

`(1)/(3)=(3)/(9)=(-4)/(-12)`

Thus, this pair has infinitely many solution.

Hence, the correct option is B.
`y=-3x+4 \ \text{and}\ \ 3y=-9x+12`