(08.01) Line M is represented by the following equation: x + y = −1 What is most likely the equation for line P so the set of equations has infinitely many solutions?

Solution:

The two lines have infinitely many Solutions, then the lines overlap at every point

To have infinitely many solutions, the lines must be identical consisting of exactly the same points to make it

Which means, in simplest form their equations are the same

x + y = -1

Multiply by 2

2x + 2y = -2

Thus, equation for line P is 2x + 2y = -2

Now we have,

Line M : x + y = -1

Lin P : 2x + 2y = -2

Similarly, we can obtain many equations for line P so that set of equations has infinitely many solutions

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation:

y = i/2 xtnop + (3i/2 tnop+ 1)

step-by-step explanation:

the picture is the step by step explanation.