Question

Which linear equations have an infinite number of solutions? Check all that apply. 

(x – ) = (x – )

8(x + 2) = 5x – 14

12.3x – 18 = 3(–6 + 4.1x)

(6x + 10) = 7(x – 2)

4.2x – 3.5 = 2.1 (5x + 8)

Answer 1

The answer is A and C. They both have infinite solutions

Answer 2

we know that

In a linear equation if the left side is equal to the right side

then

the system has an infinite number of solutions

we're going to verify every case

case A)

`(x-\ ) =(x-\ )`

In this case the left side is equal to the right side

therefore

the system case A) has an infinite number of solutions

case B)

`8(x+2)=5x-14`

`8x+16=5x-14`

In this case the left side is not equal to the right side

therefore

the system case B) does not have an infinite number of solutions

case C)

`12.3x-18=3(-6+4.1x)`

`12.3x-18=-18+12.3x`

In this case the left side is equal to the right side

therefore

the system case C) has an infinite number of solutions

case D)

`(6x+10)=7(x-2)`

`(6x+10)=(7x-14)`

In this case the left side is not equal to the right side

therefore

the system case D) does not have an infinite number of solutions

case E)

`4.2x-3.5=2.1(5x+8)`

`4.2x-3.5=10.5x+16.2`

In this case the left side is not equal to the right side

therefore

the system case E) does not have an infinite number of solutions

therefore

the answer is

`(x-\ ) =(x-\ )`

`12.3x-18=3(-6+4.1x)`