Question

Which linear equations have one solution? Check all that apply.

O 5x-1 =3(r+ 11)
O 4(r-2) + 4x = 8(x-9)
O 4(–6) + 4 = 2(r- 3)
o 2(-4) = 5(r-3) + 3
O 20-1) + 3r= 5(r-2) + 3

Answer 1

The linear equations which have one solution are C.
`4\cdot (-6) +4 = 2\cdot (r-3)`, D.
`2\cdot (-4) = 5\cdot (r-3) +3` and E.
`(20-1) +3\cdot r = 5\cdot (r-2) + 3`.

Explanation:

From Algebra we know that a system of linear equation has a unique solution when the number of variables is equal to the number of equations. Now we proceed to check if each option fulfills this condition:

A.
`5\cdot x -1 = 3\cdot (r + 11)`: Number of equations: 1/Number of variables: 2
`\{x, r\}`

B.
`4\cdot (r-2)+4\cdot x = 8\cdot (x-9)`: Number of equations: 1/Number of variables: 2
`\{x, r\}`

C.
`4\cdot (-6) +4 = 2\cdot (r-3)`: Number of equations: 1/Number of variables: 1
`\{r\}`

D.
`2\cdot (-4) = 5\cdot (r-3) +3`: Number of equations: 1/Number of variables: 1
`\{r\}`

E.
`(20-1) +3\cdot r = 5\cdot (r-2) + 3`: Number of equations: 1/Number of variables: 1
`\{r\}`

The linear equations which have one solution are C.
`4\cdot (-6) +4 = 2\cdot (r-3)`, D.
`2\cdot (-4) = 5\cdot (r-3) +3` and E.
`(20-1) +3\cdot r = 5\cdot (r-2) + 3`.