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

[939]

Homework Statement

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

Homework Equations

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

The Attempt at a Solution

It cannot be solved by elimination or substitution.

 

[LCKurtz]

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

 

[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.

 

[HallsofIvy]

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).

 

[skiller]

Oops! My "correction" was erroneous.

Apologies.

 

[Ray Vickson]

$z=x+2$

If you want to add knowledge, please don't confuse matters by getting basic things wrong.

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

 

[skiller]

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

Correct. Sorry to both you and HoI.