System of Equations...2

[nycmathguy]

 

[MathLover1]

ax +(1-a)y=1.........eq.1
(1-a)x+y=0........eq.2
------------------------------------

(1-a)x+y=0........eq.2, solve for y
y=-(1-a)x........eq.2a

substitute in eq.1

ax +(1-a)(-(1-a)x)=1.........eq.1, solve for x

ax +(1-a)(-(1-a)x)=1
ax -(a - 1)^2 x=1
(a -(a - 1)^2) x=1
(-a^2 + 3a - 1) x=1
x=1/(-a^2 + 3a - 1)

go t eq.2s and substitute x

y=-(1-a)(1/(-a^2 + 3a - 1) )........eq.2a

y=(1 - a)/(a^2 - 3 a + 1)

 

[nycmathguy]

ax +(1-a)y=1.........eq.1
(1-a)x+y=0........eq.2
------------------------------------

(1-a)x+y=0........eq.2, solve for y
y=-(1-a)x........eq.2a

substitute in eq.1

ax +(1-a)(-(1-a)x)=1.........eq.1, solve for x

ax +(1-a)(-(1-a)x)=1
ax -(a - 1)^2 x=1
(a -(a - 1)^2) x=1
(-a^2 + 3a - 1) x=1
x=1/(-a^2 + 3a - 1)

go t eq.2s and substitute x

y=-(1-a)(1/(-a^2 + 3a - 1) )........eq.2a

y=(1 - a)/(a^2 - 3 a + 1)

Is there anything in math land that you cannot do? Simply amazing.