40 points and i need this done asap 4. two lines or equations are described in each part. decide whether each system has one solution, no solution, or infinitely many solutions. show your work or explain your reasoning (use words like slope or y-intercept). (a) line a has a rate of change (slope) of 7. line b has a rate of change (slope) of -7 (b) two equations. 2x + 3y = 5.5 4x + 6y = 11 ( see the image as )

(a) One solution.

Explanation: two lines that have same slope with opposite sign will necessarily cross each other at a single point, as one is "pointing uphill" and the other "downhill."

(b)   Infinitely many solutions.

Explanation:

2x + 3y = 5.5

4x + 6y = 11   | divide by 2

-->

2x + 3y = 5.5

2x + 3y = 5.5

--> equations are identical.

2x + 3y = 2x + 3y

so any (x,y) will satisfy this equation. This means infinitely many solutions.

(c) One solution

Explanation:

Continuing the two lines it becomes obvious they will cross at one point (the solution)

(d) No solution

Explanation: If the two lines are parallel, they will never cross (by definition of "parallel"). Therefore there will be no solution to the corresponding linear system.

x = ± 6i

step-by-step explanation:

x^2 = -36

take the square root of each side

sqrt(x^2) = sqrt(-36)

we know sqrt(ab) = sqrt(a) sqrt(b)

x = ±sqrt(36) sqrt(-1)

we know that sqrt (-1) = i

x = ± 6i