Question

3 points
If 4x + 3y = 5 ; 3x- 4y = 10 find x & y by using cramer's rule .​

Answer 1

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{gathered}D=[\begin{array}{cc}3&-4\\4&3\end{array}]\end{gathered}

D=[

3

4

−4

3

]

|D|=3\times 3-(-4)\times 4=25∣D∣=3×3−(−4)×4=25

\begin{gathered}D_x=[\begin{array}{cc}10&-4\\5&3\end{array}]\end{gathered}

D

x

=[

10

5

−4

3

]

|D_x|=10\times 3-(-4)\times 5=50∣D

x

∣=10×3−(−4)×5=50

\begin{gathered}D_y=[\begin{array}{cc}3&10\\4&5\end{array}]\end{gathered}

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).

Step-by-step explanation:

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