Solve for x and y. 3x+12y=-30...(1) 6x+6y=-24...(2)

Step 1 
One approach to solving a system of linear equations is the substitution method, which involves isolating a variable, expressing it in terms of other variables, and then substituting it into another equation to find the solution.
When using addition or substitution method in order to solve a system of linear equations, if all the variables are eliminated and the resulting statement is true, i.e. it looks something like this - 0=0, or 5=5 etc., then there are infinitely many solutions as these equations are true forever and will always be intersecting each other. 
Since the graph of linear equations is a line, it is actually the intersection of the lines that each linear equation represents. If a system has infinitely many solutions, then the lines represented by these linear equations always intersect each other at every point, i.e. they are basically the same line. 
Step 2 
Given set of linear equations: 
3x+12y=-30...(1) 
6x+6y=-24...(2) 
Now, solving these equations using the method of addition. 
Multiply the equation (1) by 2: 
2[3x+12y=-30]=6x+24y=-60...(3) 
Now, multiply equation (3) by -1: 
-6x-24y=60...(4) 
Now, add equations (2) and (4): 
-18y=36 
${\displaystyle y=\frac{36}{-18}}$ 
y=-2=(-5) 
Now, substitute (5) in (4) 
-6x-24(-2)=60 
-6x+48=60 
-6x=60-48 
-6x=12 
${\displaystyle x=\frac{12}{-6}}$ 
x=-2 
Hence, the solution is: 
x=-2 
y=-2

Answer is given below (on video)