Question

How many solutions does the system have? You can use the interactive graph below to find the answer. \begin{cases} 21x+6y=42 \\\\ 7x+2y=14 \end{cases} ⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ ​ 21x+6y=42 7x+2y=14 ​ Choose 1 answer: Choose 1 answer:

Answer 1

Step-by-step explanation:

Given that:

How many solutions does the system have? You can use the interactive graph below to find the answer.

21x+6y=42

7x+2y=14

To find : No. of solutions

Solution: The graph of both lines are overlapping,as shown in attachment.

One line is red in dashed style and one is in green.

Thus,the lines have infinite many solutions.

It can be easily shown by coefficient

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

shows lines are overlapping and have infinite many solutions.

$\frac{21}{7} = \frac{6}{2} = \frac{42}{14} \\ \\ 3 = 3 = 3$

Thus,these lines are consistent and have infinite many solutions.

Hope it helps you.