systems of equations with 3 variables using substitution method

Question

I am struggling to solve the following system of equation with 3 variables. The textbook asks to use the substitution method so I would appreciate answers that use that.

I have the following 3 equations:

${5x - y = 3}$

${3x + y = 11}$

${y - 2z = -3}$

My first step is to cancel out one variable and I use the first equation:

${y = 5x - 3}$

I then substitute this into the second equation:

${3x + 5x + 3 = 11}$

=> ${8x = 8}$

=> ${x = 1}$

But the textbook gives the answers to the 3 variables as:

${{x = {7\over 4}}, {y = {23\over4}}, {z = {35\over8}}}$

I'm obviously missing something, could somebody break down how the answers where achieved?

Answer 1

When substituting into the second equation you made a sign mistake, it should be $-3$ instead of $+3$: $$3x+5x-3=11$$ $$8x=14$$ $$x=\frac{14}{8}$$ $$x=\frac{7}{4}$$

Answer 2

5x-y=3 =| y=5x-3.. Putting the value of y in equation 2...3x+y=11.. = 3x+5x-3=11=8x-3=11 or 8x=11+3=14.=| x=14/8=7/4. X=7/4,...now put the value of x in eq 1 to get y..then put the the value of y in eq 3 to get z.