I have the following 3 equations and I need to find out if they are consistent, inconsistent or dependent using the substitute method. I am using a textbook that wants you to use the substitution method so please do not offer an alternative or better method:
${5x -y = 3}$
${3x + y = 11}$
${y - 2z = -3}$
Using the 3rd equation, I can work out what y is:
${y = 2z - 3}$
if I then plug in y to the bottom equation I get:
${(2z -3) - 2z = - 3}$
So to me, this would equal:
0 - 3 = -3
So I would say the systems are dependent but according to the textbook, the systems are consistent and indeed the following 3 variables have the following results:
${{x = {7\over 4}}, {y = {23\over4}}, {z = {35\over8}}}$
I have no idea how these values are obtained due to my substitutions.
You just showed that 3rd equation is dependend with itself. You need to put $y=2z-3$ into first or second equation.