has anyone done homework 11 for im 3, or know how to do it? i need to find triples with x+y+1/2z=4 plz help me

Question

the equation is x+y+1/2z=4 the question is, "find a dozen or so different tripples that are solutions to this equation" thank you so much!!!

Answer 1

I am assuming you meant x+y+(1/2)(z)=4. If you meant x+y+1/(2z)=4, the technique still works, you will have to change my answer accordingly. The equation describes a surface in three dimensional space. A triple is a point on the surface. The easiest way to find a triple is to plug a number in for one variable (one axis), and solve the line for other points.

Let's start easy by setting z=2, that gives x+y+1=4, or y=3-x If I set x=3, then y=0 ; x=2, y=1; x=1, y=2, And so on. The triples so far are (3,0,2);(2,1,2);(1,2,2).

I'll give you another set to make it clearer: Set z=4, then x+y+2=4, or y=2-x. Set x=3, y=-1;x=2,y=0;x=1,y=1, and so on

This yields (3,-1,4);(2,0,4);(1,1,4)