Answer:x
=
6
and
y
=
−
8
through systems of equations.
Explanation:
This is known as a system of equations. For this system, we are going to use substitution, since you already know what y is equal to.
As you can see,
y
=
−
1
2
x
−
5
. Since we have
y
directly set equal to something, we can substitute it in for
y
anywhere we want. In this case we will substitute it in for
y
in your first equation.
x
−
2
y
=
2
⇒
x
−
2
(
−
1
2
x
−
5
)
=
2
Through algebraic equation steps, we can simplify the equation to be
x
+
x
−
10
=
2
, and solve the equation for
x
=
6
.
Now that we have the
x
value, we can substitute it in to the
y
equation.
y
=
−
1
2
(
6
)
−
5
When simplified, you get
y
=
−
3
−
5
, or
y
=
−
8
. And remember, if you'd like to check your answer, simply plug your numbers back in for the variables.
y
=
−
1
2
x
−
5
⇒
(
−
8
)
=
−
1
2
(
6
)
−
5
, and when simplified,
−
8
=
−
8
.x
=
6
and
y
=
−
8
through systems of equations.
Explanation:
This is known as a system of equations. For this system, we are going to use substitution, since you already know what y is equal to.
As you can see,
y
=
−
1
2
x
−
5
. Since we have
y
directly set equal to something, we can substitute it in for
y
anywhere we want. In this case we will substitute it in for
y
in your first equation.
x
−
2
y
=
2
⇒
x
−
2
(
−
1
2
x
−
5
)
=
2
Through algebraic equation steps, we can simplify the equation to be
x
+
x
−
10
=
2
, and solve the equation for
x
=
6
.
Now that we have the
x
value, we can substitute it in to the
y
equation.
y
=
−
1
2
(
6
)
−
5
When simplified, you get
y
=
−
3
−
5
, or
y
=
−
8
. And remember, if you'd like to check your answer, simply plug your numbers back in for the variables.
y
=
−
1
2
x
−
5
⇒
(
−
8
)
=
−
1
2
(
6
)
−
5
, and when simplified,
−
8
=
−
8
.
Step-by-step explanation:
