Question

Solve the system of equations by the substitution method.



Choose one answer.
a. (1, -3)
b. (3, -1)
c. infinite number of solutions
d. no solution

Answer 1

Rearrange for x on the second equation to get x=6y+6 put that into the first equation and you will get
\[(1/3)(6y+3)-2y=1-->2y+1-2y=1--->2y-2y=0-->2y=2y--->y=1 \] now substitute one in to the second equation x-6(1)=3--->x=9
The solution y=1 and x=9
9-6(1)=2
and 1/3(9)-2(1)-->3-1=1

Answer 2

as you can see :

x/3 - 2y = 1
x - 6y = 3

if you multiply the first one by 3 you get
x-6y = 3

so you have the same equation..
you have : x = 3 + 6y

which means infinite number of solutions

Answer 3

eqn 2 becomes
x=6y+3
so eqn 1 becomes
(1/3)(6y+3)-2y=1
2y+1-2y=1
1=1
which is always true, so this system has "infinite solutions"