If (2 − 3i) + (x + yi) = 6, what is x + yi?

(2 − 3i) + (x + yi) = 6

We add the left hand side

(2+x) + (-3+y)i = 6

6 can be written in a+ib

6 can be written as 6 + 0i

(2+x) + (-3+y)i = 6 +0i

Now we frame 2 equations

2 + x= 6

-3 + y =0

Solve the first equation

2 + x = 6

Subtract 2 from both sides

x = 4

solve the second equation

-3 + y =0

Add 3 on both sides

y= 3

So x+yi is 4+3i

18.75 gallons

step-by-step explanation:

graph b

step-by-step explanation:

one solution- graph a (clear intercepting point.)

no solution- graph b (they're parallel, there will never be a point of interception.)

infinite solutions- graph c (all points intercept.)