Answer the following asap
20

the graphing method is best
the substitution method is best
the elimination method is best

Graphing:  Graphing is the best method to use when introducing a new student to solving systems of two equations in two variables, because it gives them a visiual to recognize what they are looking for.  Graphing is less exact and often takes more time than the other methods.  I only recommend graphing to find a solution if the problem comes with a graph already drawn and the intersection appears to be on an exact coordinate.

Substitution:  Substition gives that advantage of having an equation alrady written for the second variable when you find the first one.  Substitution is best used when one (or both) of the equations is already solved for one of the variables.  It also works well if one of the variables has a coefficient of 1.

Elimination:  Elimination is the method that I use almost every time.  If you are not sure which method to use, I recommend that you use elimination.  Elimination is best used when both equations are in standard form (Ax + By = C).  Elimination is also the best method to use if all of the variables have a coefficient other than 1.

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!