What does y equal in the solution of the system of equations?

Question

-2x + y + 6z = 1
3x + 2y + 5z = 16
7x + 3y - 4z = 11

Answer 1

We can substitute the first equation into the other 2 equations.

 

From the first equation,

 

y = 1 + 2x - 6z

 

 

Substituting,

 

3x + 2(1 + 2x - 6z) + 5z = 16

7x - 7z = 14

 

7x + 3(1 + 2x - 6z) - 4z = 11

13x - 22z = 8

 

 

We now have 2 bolded equations with only 2 variables to work with.  Next, we can divide both sides of the first bolded equation by 7.

 

7(x - z) = 14

 

  x - z = 2

 

This becomes a fourth equation.  Substitute this equation into the second bolded equation.

 

13(2 + z) - 22z = 8

 

 

Solve for z from this equation.  When you have solved for z, plug it into the fourth equation to solve for x.  Then once you have both x and z, plug those values into the first equation to solve for y.

 

I don't know what specific value you need to solve for, by I have shown you the steps to solve for ALL of them.