Question

What is the solution of the following system?

-3x - 2y = -12
9x + 6y = -9

Answer 1

Is there a particular method we are supposed to use?

Answer 2

It does not state a method :(

Answer 3

I sense a problem with this system. After multiplying the top equation by 3 and adding the two together, it kinda falls apart.

Answer 4

Solving both equations for y to get slope-intercept form will also point out this particular feature.

Answer 5

My available answer choices are; no solutions, infinitely many solutions, (2,1) or (-2,-1)

Answer 6

Ok, in that case, elimination is probably the simplest and easiest route for this one.
You would multiply the top equation by 3 to get
\(-9x-6y=-36\)
You would add that together with the bottom equation.
\(\cancel{-9x}-\cancel{6y}=-36\)
\(\cancel{9x}+\cancel{6y}=-9\)
\(0\ne-45\)
No solution.

Answer 7

In all honesty, this problem was mostly busy work....

Answer 8

Busy work + knowledge of a concept: It's important to know what 'no solution' means in this context, i.e. the two lines are parallel (have identical slope) and therefore do not intersect.

Answer 9

Thank you all so much for your help!!!

Answer 10

True, if you solve them both out for \(y\) you should be able to see this.

\(-3x - 2y = -12\\
-2y=3x-12\\
y=\color{blue}{-\dfrac{3}{2}x}+6\)


\(9x + 6y = -9\\
6y=-9x-9\\
y=\color{blue}{-\dfrac{3}{2}x}-9\)