Question

Solve the following systems of equations using the substitution method.
What type of system is it? Name the solution if there is one.
x-y=3
x+3y=6

Answer 1

x - y = 3
x = y + 3
now sub y + 3 in for x in the other equation

x + 3y = 6
y + 3 + 3y = 6 -- subtract 3 from both sides
y + 3y = 6 - 3 -- combine like terms
4y = 3 -- divide both sides by 4
y = 3/4

now sub 3/4 in for y in either equation to find x
x - y = 3
x - 3/4 = 3
x = 3 + 3/4
x = 12/4 + 3/4
x = 15/4

check...
x + 3y = 6
15/4 + 3(3/4) = 6
15/4 + 9/4 = 6
24/4 = 6
6 = 6 (correct)

so x = 15/4 and y = 3/4

what type of system ?? I guess it is a two variable system of linear equations.

Answer 2

i think they are asking if it is constant inconsistent or dependent system? I'm not sure?

Answer 3

@texaschic101

Answer 4

sine they are both 6=6 i would guess consistent system?

Answer 5

@texaschic101