Mathematics, 07.04.2021 04:10 ella3714
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?
β
x
=
β
y
+
2
3
y
+
4
=
2
x
Ryanβs
I solved by adding the equations. The solution is
(
2
,
0
)
.
β
x
=
β
y
+
2
β
x
β
y
=
2
3
y
+
4
=
2
x
β
2
x
β
3
y
=
4
x
=
2
x
β
y
=
2
β
2
β
y
=
2
y
=
0
Jesseβs
I used matrices. The solution is
(
β
2
5
,
0
)
.
system determinant
=
[
β1 1 β2 3
]
=
β
3
β
2
=
β
5
x
-determinant
=
[
2 1 β4 3
]
=
6
β
4
=
2
y
-determinant
=
[
β1 2 β2 β4
]
=
4
β
4
=
0
x
=
β
2
5
y
=
0
Markβs
I graphed the equations. The lines intersect at
(
β
10
,
β
8
)
, so the solution is
(
β
10
,
β
8
)
.
Answers: 1
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