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

Feb 28, 2016

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

#### Explanation:

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

Comparing with ${a}_{1} + {b}_{1} = {c}_{1}$ and ${a}_{2} + {b}_{2} = {c}_{2}$

We get,
a_1 =-29 ; b_1=53 ; c_1=-26
a_2=45; b_2=26= c_2 = -1

$D = \left({a}_{1} {b}_{2}\right) - \left({a}_{2} {b}_{1}\right)$
$D = \left(- 29 \times 26\right) - \left(45 \times 53\right)$
$D = \left(- 754\right) - \left(2385\right)$
$D = - 3139$

${D}_{x} = \left({c}_{1} {b}_{2}\right) - \left({c}_{2} {b}_{1}\right)$
${D}_{x} = \left(- 26 \times 26\right) - \left(- 1 \times 53\right)$
${D}_{x} = \left(- 676\right) - \left(- 53\right)$
${D}_{x} = - 676 + 53$
${D}_{x} = - 623$

${D}_{y} = \left({a}_{1} {c}_{2}\right) - \left({a}_{2} {c}_{1}\right)$
${D}_{y} = \left(- 29 \times - 1\right) - \left(45 \times - 26\right)$
${D}_{y} = \left(29\right) - \left(- 1170\right)$
${D}_{y} = 29 + 1170$
${D}_{y} = 1199$

By Cramer's Rule

$x = {D}_{x} / D$

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

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

$y = {D}_{y} / D$

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

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