5x+3y =-11 and x + 2y = -5 cramer's rule
Answers
Answer:
The solution of given system of equations is (-1,-2).
Step-by-step explanation:
If a system of equations is
ax+by=eax+by=e
cx+dy=fcx+dy=f
then by Cramer's rule
x=\dfrac{D_x}{D} and y=\dfrac{D_y}{D}x=
D
D
x
andy=
D
D
y
where,
\begin{gathered}D_x=\left|\begin{array}{cc}e&b\\f&d\end{array}\right|\end{gathered}
D
x
=
∣
∣
∣
∣
∣
e
f
b
d
∣
∣
∣
∣
∣
\begin{gathered}D_y=\left|\begin{array}{cc}a&e\\c&f\end{array}\right|\end{gathered}
D
y
=
∣
∣
∣
∣
∣
a
c
e
f
∣
∣
∣
∣
∣
\begin{gathered}D=\left|\begin{array}{cc}a&b\\c&d\end{array}\right|\end{gathered}
D=
∣
∣
∣
∣
∣
a
c
b
d
∣
∣
∣
∣
∣
The given system of equations is
5x+3y=-115x+3y=−11
x+2y=-5x+2y=−5
Here, a=5, b=3, c=1, d=2, e=-11, f=-5.
Using Cramer's rule
\begin{gathered}D=\left|\begin{array}{cc}5&3\\1&2\end{array}\right|=10-3=7\end{gathered}
D=
∣
∣
∣
∣
∣
5
1
3
2
∣
∣
∣
∣
∣
=10−3=7
\begin{gathered}D_x=\left|\begin{array}{cc}-11&3\\-5&2\end{array}\right|=-22-(15)=-7\end{gathered}
D
x
=
∣
∣
∣
∣
∣
−11
−5
3
2
∣
∣
∣
∣
∣
=−22−(15)=−7
\begin{gathered}D_y=\left|\begin{array}{cc}5&-11\\1&-5\end{array}\right|=-25-(-11)=-14\end{gathered}
D
y
=
∣
∣
∣
∣
∣
5
1
−11
−5
∣
∣
∣
∣
∣
=−25−(−11)=−14
x=\dfrac{-7}{7}=-1x=
7
−7
=−1
y=\dfrac{-14}{7}=-2y=
7
−14
=−2
Therefore, the solution of given system of equations is (-1,-2).
#Learn more:
Solve the following simultaneous equations using cramer's rule. 5x+3y=-11 ; 2x + 4y=-10