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Solve the following simultaneous equations by using Cramers’s rule: 3x-y =7, x +4y =11 - Algebra

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Solve the following simultaneous equations by using Cramers’s rule: 3x-y =7, x +4y =11

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Solution

The given equations are
3x – y = 7…(i)
x + 4y = 11…(ii)
Equation (i) and (ii) are in standard form.

`D=|[3,-1],[1,4]|=(3xx4)-(-1xx1)=12+1=13!=0`

`D=|[7,-1],[11,4]|=(7xx4)-(-1xx11)=28+11=39`

`D=|[3,7],[1,11]|=(3xx11)-(7xx1)=33-7=26`

By Cramer’s rule, we get

`x=D_x/D and  y=D_y/D`

`x=39/13 and y=26/13`

x=3 and y=2

(x,y)=(3,2)

X = 3 and y = 2 is the solution to the given equation.

Concept: Cramer'S Rule
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