Question 950805
{{{9x+8y=7}}}
{{{18x-15y=14}}}

1. 
to solve by graphing, make table for each function, choose two values for {{{x}}}, calculate {{{y}}}, then plot points and draw lines; the point where these lines intersect will be solution to this system

{{{9x+8y=7}}}....first solve for {{{y}}}

{{{y=-(9/8)x+7/8}}}

{{{x}}}|{{{y}}}

{{{0}}}|{{{7/8}}}

{{{7/9}}}|{{{0}}}


{{{18x-15y=14}}}

{{{18x-14=15y}}}

{{{(18/15)x-14/15=y}}}

{{{(6/5)x-14/15=y}}}

{{{x}}}|{{{y}}}

{{{0}}}|{{{-14/15}}}

{{{7/9}}}|{{{0}}}

{{{drawing( 600, 600, -5, 5, -5, 5,
circle(7/9,0,.1),locate(7/9,0,p(7/9,0)),
circle(0,7/8,.1),locate(0,7/8,p(0,7/8)),
circle(0,-14/15,.1),locate(0,-14/15,p(0,-14/15)),
circle(7/9,0,.1 ),locate(7/9,0,p(7/9,0)),
 graph( 600, 600, -5, 5, -5, 5, -(9/8)x+7/8, (6/5)x-14/15)) }}} 


 the two lines intersect at the point ({{{7/9}}},{{{0}}}) 


2.
elimination 

*[invoke solving_linear_system_by_elimination 9, 8, 7, 18, -15, 14] 


3.
substitution

*[invoke solving_linear_system_by_substitution 9, 8, 7, 18, -15, 14]


Which is the best method for solving the system?
Depends on given equations. There are pros and cons for each method like:


Graphing:

Pro: gives you a visual picture of what's going on and is good for really big numbers

Con: if your graphing skills are not accurate or the solution is not at the intersection of a grid line, you have to estimate your answer.

Substitution:

Pro: Gives you an exact answer

Con: Sloppy calculations can cause incorrect answers and if one equation is not already solved for a variable (y = or x = ), you have to do extra work

Elimination

Pro: Works for any system of linear equations. After one or two steps you have a one-step equation to solve and you have half of your solution.

Con: Sloppy calculations can lead to incorrect solutions

If I need a rough idea of the solution, I graph. 
If one of the equations is already solved for {{{y}}} or for{{{ x}}}, I use substitution. 
If neither of the above is true, I use elimination. 

In this case, I prefer graphing.