Question

solve the following by crsmer's rule 3x-2y=3 , 2x+y =16
plzz solve this question step by step
fast i will mark you as brainlist

Answer 1

Hey there !

Solution:

Equation 1: ( 3x - 2y - 3 = 0 )

Equation 2: ( 2x + y - 16 = 0 )

=> a₁ = 3, a₂ = 2, b₁ = -2, b₂ = 1, c₁ = -3, c₂ = -16

Cramer's Rule:

=> a₁b₂ - a₂b₁ = D

=> c₁b₂ - c₂b₁ = D₁

=> a₁c₂ - a₂c₁ = D₂

Substituting the values, we get,

=> ( 3 × 1 ) - ( 2 × -2 ) = D

=> 3 - ( -4 ) = D

=> 3 + 4 = D

=> 7 = D

____________________________________________________

=> ( -3 × 1 ) - ( -16 × -2 ) = D₁

=> ( -3 ) - ( 32 ) = D₁

=> -35 = D₁

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=> ( 3 × -16 ) - ( 2 × -3 ) = D₂

=> ( -48 ) - ( -6 ) = D₂

=> -48 + 6 = D₂

=> -42 = D₂

_____________________________________________________

Now we have got our values. According to cramer's rule,

$x = \dfrac{ D_1}{D} \:\:\: and \:\:\: y = \dfrac{D_2}{D}$

Substituting them we get,

$\implies x = \dfrac{ -35}{7} = -5 \\ \\ \implies y = \dfrac{ -42}{7} = -6$

Hence x = -5 and y = -6.

Hope my answer helped !

Answer 2

Answer:

I hope you will like this

Step-by-step explanation:

a1=3

a2=2

b1=-2

b2=1

c1=3

c2=16

D=a1 b1

a2 b2

=3 -2

2 -1

=(3×1)-(2×(-2))

=3-(-4)

=7

Dc=c1 b1

c2 b2

=3 -2

16 1

=(3×2)-(16×(-2))

=3-(-32)

=35

Dy=a1 c1

a2 c2

=3 3

2 16

=(3×16)-(2×3)

=48-6

=42

By Cramer's rule,

x=Dx÷D = 35÷7

x=5

y=Dy÷D = 42÷7

y=6

Solution: (x,y)=(5,6)

I hope you will like this