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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

Sagot :

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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].

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