# 2x + y = 8, x - z = 2. Solve by elimination and substitution

1. Mar 2, 2014

### 939

1. The problem statement, all variables and given/known data

2x + y = 8, x - z = 2. Solve by elimination and substitution

2. Relevant equations

2x + y = 8, x - z = 2

3. The attempt at a solution

It cannot be solved by elimination or substitution.

Last edited: Mar 2, 2014
2. Mar 2, 2014

### LCKurtz

You can solve for y and z in terms of x.

3. Mar 3, 2014

### skiller

To add to LCKurtz's response, you have two equations with three variables. You can solve for any of the following:

• $x$ and $y$ in terms of $z$
• $x$ and $z$ in terms of $y$
• $y$ and $z$ in terms of $x$
But you cannot solve for all three.

4. Mar 3, 2014

### HallsofIvy

Staff Emeritus
What I would do is say that, from the first equation, y= 8- 2x, and from the second equation, z= x- 2.

That is, any (x, y, z) satisfying these equations is of the form (x, 8- 2x, x- 2).

Or if you prefer "parametric equations", (x, y, z) satisfies those equation if and only if x= t, y= 8- 2t, and z= t- 2. Those points lie on a straight line in "three-space". Geometrically, a line is determined by two points. This line is the line that passes through (0, 8, -2) and (2, 4, 0).

5. Mar 3, 2014

### skiller

Oops! My "correction" was erroneous.

Apologies.

Last edited: Mar 3, 2014
6. Mar 3, 2014

### Ray Vickson

Everything HallsofIvy said was 100% correct. Where do you think he was wrong?

7. Mar 3, 2014

### skiller

Correct. Sorry to both you and HoI.