Answer:
The linear equations which have one solution are C. [tex]4\cdot (-6) +4 = 2\cdot (r-3)[/tex], D. [tex]2\cdot (-4) = 5\cdot (r-3) +3[/tex] and E. [tex](20-1) +3\cdot r = 5\cdot (r-2) + 3[/tex].
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. [tex]5\cdot x -1 = 3\cdot (r + 11)[/tex]: Number of equations: 1/Number of variables: 2 [tex]\{x, r\}[/tex]
B. [tex]4\cdot (r-2)+4\cdot x = 8\cdot (x-9)[/tex]: Number of equations: 1/Number of variables: 2 [tex]\{x, r\}[/tex]
C. [tex]4\cdot (-6) +4 = 2\cdot (r-3)[/tex]: Number of equations: 1/Number of variables: 1 [tex]\{r\}[/tex]
D. [tex]2\cdot (-4) = 5\cdot (r-3) +3[/tex]: Number of equations: 1/Number of variables: 1 [tex]\{r\}[/tex]
E. [tex](20-1) +3\cdot r = 5\cdot (r-2) + 3[/tex]: Number of equations: 1/Number of variables: 1 [tex]\{r\}[/tex]
The linear equations which have one solution are C. [tex]4\cdot (-6) +4 = 2\cdot (r-3)[/tex], D. [tex]2\cdot (-4) = 5\cdot (r-3) +3[/tex] and E. [tex](20-1) +3\cdot r = 5\cdot (r-2) + 3[/tex].
