Question

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

Answer 1

Answer:

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. $(20-1) +3\cdot r = 5\cdot (r-2) + 3$.

Step-by-step 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. $(20-1) +3\cdot r = 5\cdot (r-2) + 3$.