What is the solution to the system of equations -2x-y=1 -6x=3y+3

−
2
x
−
y
=
1
;
−
6
x
=
3
y
+
3

Step: Solve
−
2
x
−
y
=
1
for y:
−
2
x
−
y
=
1
−
2
x
−
y
+
2
x
=
1
+
2
x
(Add 2x to both sides)
−
y
=
2
x
+
1
−
y
−
1
=
2
x
+
1
−
1
(Divide both sides by -1)
y
=
−
2
x
−
1

Step: Substitute
−
2
x
−
1
for
y
in
−
6
x
=
3
y
+
3
:
−
6
x
=
3
y
+
3
−
6
x
=
3
(
−
2
x
−
1
)
+
3
−
6
x
=
−
6
x
(Simplify both sides of the equation)
−
6
x
+
6
x
=
−
6
x
+
6
x
(Add 6x to both sides)
0
=
0

Infinitely many solutions.