Answer:
[tex]6x-6y-16=0[/tex]
Step-by-step explanation:
Consider the following system of equations:
[tex]a_1x+b_1y+c_1=0\\\\a_2x+b_2y+c_2=0[/tex]
The system of equations has infinite solutions if [tex]\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}[/tex]
One equation is [tex]3x-3y=8[/tex]
[tex]3x-3y-8=0[/tex]
Take another equation as [tex]6x-6y-16=0[/tex]
So, the two equations are [tex]3x-3y-8=0[/tex] and [tex]6x-6y-16=0[/tex]
[tex]a_1=3,b_1=-3,c_1=-8,a_2=6,b_2=-6,c_2=-16[/tex]
[tex]\frac{a_1}{a_2}=\frac{3}{6}=\frac{1}{2}\\ \frac{b_1}{b_2}=\frac{-3}{-6}=\frac{1}{2}\\ \frac{c_1}{c_2}=\frac{-8}{-16}=\frac{1}{2}[/tex]
So,
[tex]\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}[/tex]
Therefore, another equation can be [tex]6x-6y-16=0[/tex]
