Question

What is the solution of the following system?

Answer 1

pick a method, substitution, or elimination and i will go through it

Answer 2

colinear factor of -3 all (x,y)

Answer 3

Substitution

Answer 4

get it into the form x=ay+b
or y=ax+b
where b is a constant

so we have

3x+3y=10
-9x-9y=-30

so let's rearrange the first equation

3x+3y=10
3y=10-3x
y=(10-3x)/3

substitute y=(10-3x)/3 into the second equation to get

-9x-9(10-3x)/3 = -30

-9x-3(10-3x)=-30
-9x-30+9x=-30
-30=-30

hence both equations are the same line

we can tell this from the start since 3x+3y=10, if we multiply by -3, we get -9x-9y=-30

hence -9x-9y=-9x-9y

so this means that there are an infinite number of solutions since all solutions are on this straight line hence infinite solutions