Question

How many intersections are there of the graphs of the equations below? x + 5y = 6 3x + 30y = 36

Answer 1

D) infinitely many

Hope this helped!

Answer 2

Answer: Option 'B' is correct.

Step-by-step explanation:

Since we have given that

$x+5y=6\\\\and\\\\3x+30y=36$

We need to find that " How many solutions are there ?"

First we compare the coefficients of x and y :

$a_1x+b_1y=c_1\\\\and,\\\\a_2x+b_2y=c_2$

Now,

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

Here,

$a_1=1,a_2=5,c_1=-6\\\\and\\\\a_2=3,b_2=30,c_2=36$

so,  it becomes,

$\frac{1}{3}=\frac{5}{30}=\frac{-6}{-36}\\\\\frac{1}{3}\neq \frac{1}{6}=\frac{1}{6}$

So, it becomes intersecting lines . So, they have unique solution.

Hence, Option 'B' is correct.