3x - 4y =10 : 4x +3y =5
solve using Cramer's rule
Answers
Answer:
The solution of the system of equations is (2,-1).
Step-by-step explanation:
The given equations are
3x-4y=103x−4y=10
4x+3y=54x+3y=5
Coefficient matrix is
\begin{lgathered}D=\left[\begin{array}{cc}3&-4\\4&3\end{array}\right]\end{lgathered}
D=[
3
4
−4
3
]
|D|=3\times 3-(-4)\times 4=25∣D∣=3×3−(−4)×4=25
\begin{lgathered}D_x=\left[\begin{array}{cc}10&-4\\5&3\end{array}\right]\end{lgathered}
D
x
=[
10
5
−4
3
]
|D_x|=10\times 3-(-4)\times 5=50∣D
x
∣=10×3−(−4)×5=50
\begin{lgathered}D_y=\left[\begin{array}{cc}3&10\\4&5\end{array}\right]\end{lgathered}
D
y
=[
3
4
10
5
]
|D_y|=3\times 5-10\times 4=15-40=-25∣D
y
∣=3×5−10×4=15−40=−25
x=\frac{|D_x|}{|D|}=\frac{50}{25}=2x=
∣D∣
∣D
x
∣
=
25
50
=2
y=\frac{|D_y|}{|D|}=\frac{-25}{25}=-1y=
∣D∣
∣D
y
∣
=
25
−25
=−1
Therefore the solution of the system of equations is (2,-1).