Solving Systems of Equations by Substitution 1. y = 6x − 11
2. −2x − 3y = −7
3. y = −3x + 5
4. 5x − 4y = −3
5. y = −2
6. 4x − 3y = 18
7. −4x + y = 6
8. −5x − y = 21
9. 2x − 3y = −1
10. y = x − 1
11. −3x − 3y = 3
12. y = −5x − 17
13. y = 5x − 7
14. −3x − 2y = −12
15. −7x − 2y = −13
16. x − 2y = 11

answer: a. 74

step-by-step explanation:

it shows divided evenly, so add the 37+37 = 74

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!

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:

large crystals result from very slow cooling.

evaporation of water: this would produce an evaporite which is a sedimentary rock. like a salt pan in a desert. not possible to have volcanic rocks originate this way.

crystalization in molten earth: slow cooling over time. (hundreds to millions of years)

crystalization at earth's surface: this results in fast cooling. (a few hours to a few months or years)

crystalization from cooling off hot water: that would be a hydrothermal deposit. while associated with volcanics they are not volcanic rocks themselves and usually occur fairly rapidly.