Respuesta :
The coordinates of a point are written in the form:
[tex](x,y)[/tex]Substitute the values of x and y of each given option to check if they satisfy the equation or not.
a)
x=2 and y=38
[tex]\begin{gathered} -2(7(2)+3(38))=86 \\ \Rightarrow-2(14+114)=86 \\ \Rightarrow-2(128)=86 \\ \Rightarrow-256=86 \end{gathered}[/tex]This point does not satisfy the equation.
b)
x=1 and y=-24
[tex]\begin{gathered} -2(7(1)+3(-24))=86 \\ \Rightarrow-2(7-72)=86 \\ \Rightarrow-2(-65)=86 \\ \Rightarrow130=86 \end{gathered}[/tex]This point does not satisfy the equation.
c)
x=-1 and y=-12
[tex]\begin{gathered} -2(7(-1)+3(-12))=86 \\ \Rightarrow-2(-7-36)=86 \\ \Rightarrow-2(-43)=86 \\ \Rightarrow86=86 \end{gathered}[/tex]This point satisfies the equation.
d)
x=-2 and y=-9
[tex]\begin{gathered} -2(7(-2)+3(-9))=86 \\ \Rightarrow-2(-14-27)=86 \\ \Rightarrow-2(-41)=86 \\ \Rightarrow82=86 \end{gathered}[/tex]This point does not satisfy the equation.
Therefore, the only option which satisfies the given equation, is:
[tex]c.(-1,-12)[/tex]