Question

6x-3y=-10 ; 3x+5y-8=0. Solve this equations by Cramer’s method.

Answer 1

Given,
6x - 3y = -10
3x + 5y - 8 = 0

arrange both equations in general form ax + by + c = 0 .
e.g., 6x - 3y + 10 = 0 -----(1)
3x + 5y - 8 = 0 -----(2)
now, use Cramer's rule,
$\bold{\frac{x}{-3\times-8-10\times5}=\frac{-y}{6\times-8-10\times3}=\frac{1}{6\times5-(-3)\times3}}$
=> x/(24 - 50) = -y/(-48 - 30) = 1/(30 +9)

=> x/-26 = -y/-78 = 1/39

=> x = -26/39 = -2/3 and y = 78/39 = 2

hence, x = -2/3 and y = 2

Answer 2

solution:-

given by :-
$6x - 3y = - 10.........(1) \\ 3x + 5y = 8............(1) \\ solving \: eq \: (1) \: and \: (2) \: by \: cramers \: method \\ Δ = \binom{6 \: \: \: - 3}{3 \: \: \: \: \: 5} = 30 + 9 = 39 \\ Δx = \binom{ - 10 \: \: \: - 3}{ 8 \: \: \: \: \: \: \: \: 5} = - 50 + 24 = - 26 \\ Δy = \binom{6 \: \: \: - 10}{ 3 \: \: \: \: \: \: \: \: 8} = 48 + 30 = 78 \\ x = \frac{Δx}{Δ} = \frac{ - 26}{39} = - \frac{2}{3} \\ \\ y = \frac{Δy}{Δ} = \frac{78}{39} = 2$
here ( x , y) = ( -2/3 , 2)

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