Question

Solve the following simultaneous equations using Cramer’s Rule.

5x + 3y = -11 ; 2x + 4y = -10​

Answer 1

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Solution : Given equations

5x + 3y = -11

2x + 4y = -10

D =

5 3

2 4 = (5 ´ 4) - (2 ´ 3) = 20 - 6 = 14

Dx =

-11 3

-10 4 = (-11) ´ 4 - (-10) ´ 3 = -44 -(-30)

= -44 + 30

= -14

Dy = 5 -11

2 -10 = 5 ´ (-10) - 2 ´ (-11) = -50 -(-22)

= -50 + 22 = -28

x = Dx

D = −14

14 = -1 and y = Dy

D = −28

14 = -2

(x, y) = (-1, -2) is the solution.

Answer 2

Solve the following simultaneous equations using Cramer’s Rule.

5x + 3y = –11 ; 2x + 4y = –10

Solution:

5x + 3y = –11

2x + 4y = –10

( ) ( )

( )

D 5 3

3

D 4 3 44 30

10

5

D 10 2 50 22

2

and

x

y

x y

= =  −  = − =

= =  −  = − = − + =

−

= =  − −  = − = − + =

= = = =

(x, y) = ( , )is the solution.