Question

x+y-8/2=x+2y-14/3=3x-y/4. Solve this equations by Cramer’s method.

Answer 1

Solution:-

given by:-
$\frac{x + y - 8}{2} = \frac{3x - y}{4} \\ 4x + 4y - 32 = 6x - 2y \\ - 2x + 6y = 32 \\ x - 3y = - 16........(1) \\ \frac{x + 2y - 14}{3} = \frac{3x - y}{4} \\ 4x + 8y - 56 = 9x - 3y \\ - 5x + 11y = 56 \\ 5x - 11y = - 56...........(1) \\ solving eq(1) and eq(2) by cramer's method \\ Δ = \binom{1 \: \: \: \: \: \: - 3}{5 \: \: - 11} = - 11 + 15 = 4 \\ Δx = \binom{ - 16 \: \: \: - 3}{ - 56 \: \: \: -11} = 176 - 168 = 8$
$Δy = \binom{1 \: \: \: - 16}{5 \: \: \: - 56} = - 56 + 80 = 24 \\ x = \frac{Δx}{Δ} = \frac{8}{4} = 2 \\ y = \frac{Δy}{Δ} = \frac{24}{4} = 6$
here (x ,y ) = (2 ,6)

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