Question

A system has an infinite number of solutions. one equation is 3x-3y=8. Which could be the other equation in the system of equations?

Answer 1

Answer:

$6x-6y-16=0$

Step-by-step explanation:

Consider the following system of equations:

$a_1x+b_1y+c_1=0\\\\a_2x+b_2y+c_2=0$

The system of equations has infinite solutions if $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

One equation is $3x-3y=8$

$3x-3y-8=0$

Take another equation as $6x-6y-16=0$

So, the two equations are $3x-3y-8=0$ and $6x-6y-16=0$

$a_1=3,b_1=-3,c_1=-8,a_2=6,b_2=-6,c_2=-16$

$\frac{a_1}{a_2}=\frac{3}{6}=\frac{1}{2}\\ \frac{b_1}{b_2}=\frac{-3}{-6}=\frac{1}{2}\\ \frac{c_1}{c_2}=\frac{-8}{-16}=\frac{1}{2}$

So,

$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

Therefore, another equation can be $6x-6y-16=0$