What is the Solution of the following system?

{-3x - 2y = - 12

{9x + 6y = - 9

Imagine those two bracket things are one big one connecting both equations, and the answers are A (2,1) B No Solutions C (-2, - 1) D Infinitely Many Solutions

@ Emma11234

The given system is called a system of linear equations in 2 variables.

One of the methods we can use to solve the system is the elimination method. In this method we multiply one of the equations with a certain value, such that when the this equation is added to the other one, one of x or y cancels out:

Notice that we can eliminate the variable y by multiplying the first equation by 3, and adding it to the second equation:

the system becomes:

-9x-6y=-36

9x+6y=-9

adding the left hand sides, and the right hand sides of the equations we have:

0=-45, which is not true. This means that the system has no solutions because all the operations we used are valid, but the result is absurd.

Answer: B. No solutions.

Remark:

we could have noticed that the coefficients of x and y in both equations are proportional. (-3 * (-3) = 9, - 2 * (-3) = 6)

In such situations, if the numbers in the right hand side are also proportional, then the solution has infinitely many solutions,

if not, as in our case, the system has no solution.