Question

What is the solution of the following system?
-2x-y=1
-4x-2y=-1

Answer 1

A. Infinitely many solutions
B. No solution
c. (3,8)
D. (-3, -8)

Answer 2

It can be solved by 2 methods :

i) Substitution
ii) Elimination .

Do you know both of these methods? If yes, then which one you want to solve with.

Answer 3

Ok, good question. No need to solve this.

See, do you know the formula for checking whether there will be no solution, infinitely many solutions or some solution...

Answer 4

Uhm, No I do not..

Answer 5

Ok, suppose I have two equations:

\(\color{blue}{\large a_1 x + b_1 y = c_1}\\
\large{\color{red}{a_2 x + b_2 y = c_2 } }\)

Then:

\(\large \color{blue}{i) \space \textbf{If :} \cfrac{a_1}{a_2} \ne \cfrac{b_1}{b_2} \ne \cfrac{c_1}{c_2} \implies \textbf{The equations will have some solutions}} \\
\color{red}{ii) \space \textbf{If : } \cfrac{a_1}{a_2} = \cfrac{b_1}{b_2} \ne \cfrac{c_1}{c_2} \implies \textbf{The equations will have no solution }} \\
\color{orange}{iii) \space \textbf{If :} \cfrac{a_1}{a_2} = \cfrac{b_1}{b_2} = \cfrac{c_1}{c_2} \implies \textbf{The equations will have infinitely many solutions}} \)

Answer 6

Please notice the formula again, I had edited the mistake there. Sorry for inconvenience

Now, in : -2x - y = 1 , can you tell me what is \(a_1\) , \(b_1\) , \(c_1\) ... ? by comparing it with

\(a_1x+b_1 y = c_1\)

Answer 7

@SamiiBelle ?

Answer 8

Thank you for this. I worked the problem out with my dad and I got No solutions.

Answer 9

Good work, yes it is No Solutions. :) Give a "thumbs up" to your dad too :)

Answer 10

Thanks for the metal! @mathslover