Ryan, Jesse, and Mark each solved this system of equations. All of their answers are different. Find and explain the mistakes. What is the correct answer?


−
x
=
−
y
+
2



3
y
+
4
=
2
x

Ryan’s answer:
I solved by adding the equations. The solution is
(
2
,
0
)
.


−
x
=
−
y
+
2

→

x
−
y
=
2

3
y
+
4
=
2
x

→

2
x
−
3
y
=
4

x
=
2

x
−
y
=
2

→

2
−
y
=
2

y
=
0

Jesse’s answer:
I used matrices. The solution is
(
−
2
5
,
0
)
.


system determinant
=
[
−1 1 −2 3
]
=
−
3
−
2
=
−
5


x
-determinant
=
[
2 1 −4 3
]
=
6
−
4
=
2


y
-determinant
=
[
−1 2 −2 −4
]
=
4
−
4
=
0


x
=
−
2
5


y
=
0



Mark’s answer:
I graphed the equations. The lines intersect at
(
−
10
,
−
8
)
, so the solution is
(
−
10
,
−
8
)
.