Solve by Cramer's rule,2x+3y=2,2x-y=1
Answers
Step-by-step explanation:
The given equations are as follows-
(1) 2x+3y=22x+3y=2
(2) x- \frac{y}{2}= \frac{1}{2}x−
2
y
=
2
1
By Cramer's Rule,
\begin{gathered}I = \left|\begin{array}{ccc}2&3\\1& -\frac{1}{2} \end{array}\right| = -4\end{gathered}
I=
∣
∣
∣
∣
∣
2
1
3
−
2
1
∣
∣
∣
∣
∣
=−4
\begin{gathered}I_{x} = \left|\begin{array}{ccc}2&3\\\frac{1}{2}& -\frac{1}{2} \end{array}\right| = -2.5\end{gathered}
I
x
=
∣
∣
∣
∣
∣
2
2
1
3
−
2
1
∣
∣
∣
∣
∣
=−2.5
\begin{gathered}I_{y} = \left|\begin{array}{ccc}2&2\\1& \frac{1}{2} \end{array}\right| = -1\end{gathered}
I
y
=
∣
∣
∣
∣
∣
2
1
2
2
1
∣
∣
∣
∣
∣
=−1
As I ≠ 0, the given set of equations are consistent and have an independent solution.
Hence, by Cramer's Rule,
x= \frac{ I_{x} }{I} = \frac{-2.5}{-4} = 0.625 = \frac{5}{8}x=
I
I
x
=
−4
−2.5
=0.625=
8
5
y= \frac{ I_{y} }{I} = \frac{-1}{-4} = 0.25 = \frac{1}{4}y=
I
I
y
=
−4
−1
=0.25=
4
1
So, the solution set is (0.625, 0.25)
[ANSWERED]
Enter a problem...
Precalculus Examples
Popular Problems Precalculus Solve Using a Matrix with Cramer's Rule 2x+3y=11 , x-2y=7
2
x
+
3
y
=
11
,
x
−
2
y
=
7
Represent the system of equations in matrix format.
[
2
3
1
−
2
]
[
x
y
]
=
[
11
7
]
The determinant of
[
2
3
1
−
2
]
is
−
7
.
Tap for more steps...
D
=
−
7
The determinant of
[
11
3
7
−
2
]
is
−
43
.
Tap for more steps...
D
x
=
−
43
The determinant of
[
2
11
1
7
]
is
3
.
Tap for more steps...
D
y
=
3
Find the value of
x
by Cramer's Rule, which states that
x
=
D
x
D
. In this case,
x
=
−
43
−
7
.
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x
=
43
7
Find the value of
y
by Cramer's Rule, which states that
y
=
D
y
D
. In this case,
y
=
3
−
7
.
Tap for more steps...
y
=
−
3
7
The solution to the system of equations using Cramer's Rule.
x
=
43
7
,
y
=
−
3
7
image of graph