How do you solve the following system?: $- 29 x + 53 y = - 26, 45 x + 26 y = - 1$ $-29x +53y =-26 , 45x +26y = -1$

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How do you solve the following system?: $- 29 x + 53 y = - 26, 45 x + 26 y = - 1$ $-29x +53y =-26 , 45x +26y = -1$

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Answer 1 · 2016-02-28T06:55:21

$x = \frac{623}{3139}$ $x= 623/3139$ & $y = - \frac{1199}{3139}$ $y=-1199/3139$

Explanation:

$- 29 x + 53 y = - 26$ $-29x+53y=-26$ -----------------------------------------(1)
$45 x + 26 y = - 1$ $45x+26y = -1$ ------------------------------------------(2)

Comparing with $a_{1} + b_{1} = c_{1}$ $a_1+b_1=c_1$ and $a_{2} + b_{2} = c_{2}$ $a_2+b_2=c_2$

We get,
$a_{1} = - 29; b_{1} = 53; c_{1} = - 26$ $a_1 =-29 ; b_1=53 ; c_1=-26$
$a_{2} = 45; b_{2} = 26 = c_{2} = - 1$ $a_2=45; b_2=26= c_2 = -1$

$D = (a_{1} b_{2}) - (a_{2} b_{1})$ $D =(a_1b_2)-(a_2b_1)$
$D = (- 29 \times 26) - (45 \times 53)$ $D= (-29xx26) - ( 45xx53)$
$D = (- 754) - (2385)$ $D= (-754) - (2385)$
$D = - 3139$ $D= -3139$

$D_{x} = (c_{1} b_{2}) - (c_{2} b_{1})$ $D_x = (c_1b_2)-(c_2b_1)$
$D_{x} = (- 26 \times 26) - (- 1 \times 53)$ $D_x = (-26xx26)-(-1xx53)$
$D_{x} = (- 676) - (- 53)$ $D_x = (-676)-(-53)$
$D_{x} = - 676 + 53$ $D_x = -676+53$
$D_{x} = - 623$ $D_x = -623$

$D_{y} = (a_{1} c_{2}) - (a_{2} c_{1})$ $D_y=(a_1c_2)-(a_2c_1)$
$D_{y} = (- 29 \times - 1) - (45 \times - 26)$ $D_y=(-29xx-1)-(45xx-26)$
$D_{y} = (29) - (- 1170)$ $D_y=(29)-(-1170)$
$D_{y} = 29 + 1170$ $D_y=29+1170$
$D_{y} = 1199$ $D_y=1199$

By Cramer's Rule

$x = \frac{D_{x}}{D}$ $x= D_x/D$

$x = \frac{- 623}{- 3139}$ $x=(-623)/-3139$

$x = \frac{623}{3139}$ $x= 623/3139$

$y = \frac{D_{y}}{D}$ $y=D_y/D$

$y = \frac{1199}{- 3139}$ $y=1199/-3139$

$y = - \frac{1199}{3139}$ $y=-1199/3139$

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How do you solve the following system?: $- 29 x + 53 y = - 26, 45 x + 26 y = - 1$ $-29x +53y =-26 , 45x +26y = -1$

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How do you solve the following system?: -29x +53y =-26 , 45x +26y = -1−29x+53y=−26,45x+26y=−1 -29x +53y =-26 , 45x +26y = -1

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How do you solve the following system?: $- 29 x + 53 y = - 26, 45 x + 26 y = - 1$ $-29x +53y =-26 , 45x +26y = -1$