Question

solve by Cramer's rule
$x - y = 10 \: \: \: \: \: \: \: \: \: 2x + 5y = 8$
​

Answer 1

Answer:

x= -4/7

y= 58/7

Step-by-step explanation:

let's

x−y=10 eq. (i)

2x+5y=8 eq. (ii)

convert into matrix form

$\binom{1 \: \: - 1}{2 \: \: \: 5} \binom{x}{y} = \binom{10}{8}$

AX=B

$A = \binom{1 \: \: - 1}{2 \: \: \: 5}$

$X = \binom{x}{y}$

$B = \binom{10}{8}$

Let's Det A

$det \: A = \binom{1 \: \: - 1}{2 \: \: \: 5}$

=(1x5)-(-1x2)

=5+2

=7

$det \: D¹ = \binom{1 \: \: 10}{2 \: \: \: 8}$

=(1x8)-(10x2)

=8-12

=-4

$det \: D² = \binom{10 \: \: \: - 1}{8 \: \: \: 5}$

=(10x5)-(-1x8)

=50+8

=58

$x = \frac{D¹}{det \: a} \\ x = \frac{ - 4}{7}$

$y = \frac{D²}{det \: a} \\ y = \frac{58}{7}$