Question

5x+2y=7; 6x-5y=38 solve this by using cramer's rule
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Answer 1

Answer:

The solution of 5x+2y=7 and 6x-5y=38 is

Answer 2

Answer:

values are x = 3 and y = -4

Step-by-step explanation:

given equations are:

5x + 2y = 7

6x - 5y = 38

let us solve this using crammers rule :

matrix A = $\left[\begin{array}{cc}5&2\\6&-5\end{array}\right]$

determinant of matrix A is (5)(-5) - (6)(2) = - 25 - 12 = - 37

|A| = -37

D = $\left[\begin{array}{ccc}7\\38\end{array}\right]$

X = $\left[\begin{array}{ccc}x\\y\end{array}\right]$

replace ( 7 , 38 ) in place of ( 5 , 6 ) in matrix A to get A₁

A₁ = $\left[\begin{array}{ccc}7&2\\38&-5\end{array}\right]$

determinant of A₁ = (7)(-5) - (38)(2)

|A₁| = -35 - 76 = - 111

replace ( 7 , 38 ) in place of ( 2 , -5 ) in matrix A to get A₂

A₂ = $\left[\begin{array}{ccc}5&7\\6&38\end{array}\right]$

determinant of A₂ is (5)(38) - (7)(6)

|A₂| = 190 - 42

|A₂| = 148

formula to find 'x' and 'y' are :

x = |A₁|/|A|

y = |A₂|/|A|

x = -111/-37 = 111/37 = 3

y = 148 / -37 = -4

values are x = 3 and y = -4