Given the equation [tex]6x-3y=5.[/tex]
Check all options:
A. [tex]\left(9,\dfrac{16}{3}\right)[/tex], this means that [tex]x=9, y=\dfrac{16}{3}.[/tex] Substitute these numbers into the left side of the equation equation:
[tex]6\cdot 9-3\cdot \dfrac{16}{3}=54-16=38\neq 5.[/tex]
This option is false.
B. [tex]\left(6,-3\right)[/tex], this means that [tex]x=6, y=-3.[/tex] Substitute these numbers into the left side of the equation equation:
[tex]6\cdot 6-3\cdot (-3)=36+9=45\neq 5.[/tex]
This option is false.
C. [tex]\left(1,-\dfrac{11}{3}\right)[/tex], this means that [tex]x=1, y=-\dfrac{11}{3}.[/tex] Substitute these numbers into the left side of the equation equation:
[tex]6\cdot 1-3\cdot \left(-\dfrac{11}{3}\right)=6+11=17\neq 5.[/tex]
This option is false.
D. [tex]\left(-2,-\dfrac{17}{3}\right)[/tex], this means that [tex]x=-2, y=-\dfrac{17}{3}.[/tex] Substitute these numbers into the left side of the equation equation:
[tex]6\cdot (-2)-3\cdot \left(-\dfrac{17}{3}\right)=-12+17=5.[/tex]
This option is true.
Answer: correct choice is D.
Answer:
Option d
Step-by-step explanation:
Given is a linear equation in x and y as
[tex]6x-3y =5[/tex]
To check whether a point satisfies the equation, let us substitute and check whether the equation holds good
a) [tex]6(9)-3(16/3) = 38 \neq 5[/tex]
b) [tex]6(6)-3(-3) \neq 5[/tex]
c) [tex]6(1)-3(-11/3) = 17\neq 5[/tex]
d) [tex]6(-2)-3(-17/3) = -12+17 =5[/tex]
Since last point satisfies the equation, option d is the answer.
