Solving Linear Systems Without.

One way to solve a linear eqaution without gragping it is by
rewqrewrewqrweqrewqsubstitution!!
For Example: 3x+4y=-4 AND x+2y=2
nsmfjStep 1) solve one equationffor one fdsfdasfdffvariable (x+2y=2)
fdsafdsfdsfdsfdsfds x=-2y+2
nfdj step 2) substitute x=-2y+2 in for x on gfdgfdgfd.the second equation
fdsafdsfdsfdsfsdaf s3(-2y+2)+4y=-4
gfasfdsamultiply and add like terms
dfdsafsdafdsafds fd-6y+6+4y=-4
hjfhfhhhjhgjhgjgfgfa-2y=-10
hgdgdfgfhgfhgfhgfhfgy=5
fdsfstep 3) substitute the value from gfdgfdgfdstep 2 (y=5) into .the equation gfdgfdgfdfrom step 1 and solve
fdsafsdafasdfsdafdsx=-2(5)+2
gfsdgdfsgfdsgdfgfdg x=-8
gfdsgfd

gfdggggThe answer is... (-8,5)
dasfdsafsdafdsdsfdasfdsafsdafdsaf

Linear Combination is another way to solve equations.

fdsfaThe first step is to multiply nor or both equations by a constant to obtain coefficients that differ only in signs for one variable.
fdsfsfdsafsdaff2x-4y=13
fdsfdsfdsfdsfd 4x-5y=8
fsdafdsMultiply the first equation by -2 so that it will be
fdsfdsfdsfdsaff-4x+8y=-26
gfgdfgdfgdfggs4x-5y=8
fdsafs After you multiply and get your revised equation, add the two new ones together and solve for one variable.
fdsafsdfsdffdsf-4x+8y=-26
hjkljkljkhjklhj4x-5y=8
fdsfsd gfdgdfgg3y=-18
gfdgfdgdfgggggy=-6
fdgdfgThe last step is to plug in y=-6 into your orginal equation and find the value of x!
gfdgdfgdfgg2x-4y=13
fdsafdsfsdf2x-4(-6)=13
gfdgdfgdfgs2x+24=13
fdsfdsfdsfds2x=37
fgdsfgdfsgdsfx=-11/2
rewrThe answer is (-11/2,-6)

and now for a word problem...
ghsyou enroll in a book club in which you can earn bonus points to use toward the purchase of books. each book you order costs $6.95 and earns you 2 bonus points. each hardcover bood costs $19.95 and earns you 4 bonus points. the first order you place comes to a total of $60.75 and earns you 14 bouse points. how many of each type of bood did you order?
gfdgstep 1)Multiply how many paperbacks you ffffffffffgetting and thefprice of them together and ffffffffffdo the same for the hardcover books and dddd.add them together to get your first equation.
hjklhhjkl$6.95xf+ $19.95y = $60.75
rqrwestep 2) Multiple the number of bonus points ffffffffffrecievedfto the number of paperbacks (x) ffffffffffand hardcovers (y) for.you second equation.
fdfdsfd 2x+4y=14
fdsfddstep3) Solve for one of the variables
fdsfdsfs2x+4y=14 becomes 2x=14-4y simplify fffffffffffyour answer and it is
fdsfdsfsdfsdfsdfsdf dx=7-2y
dsasf step 4) Replace x with you your new dddd.equation x=7-2y intofequation one.
fffdsfdsf$6.95(7-2y) + $19.95y = $60.75
fdfdsfda48.65 -13.90y +19.95y = 60.75
fdsfsf sa6.05y =12.10
fdsdafd. y =2
trewttstep 5) Put y = 2 back into equation one fffffffffand find x
ffdafdasf 6.95x + 19.95(2) = 60.75
gfdsfgs ..6.95x + 39.90 = 60.75
fdafsfs..,.6.95x = 20.85
gfgad rfafx = 3
fdsfddthe answer is... (3,2)
ffffdsfasdfsdfds51 2dfd +fdsthe

and finally a graphing problem!
gfdgyou have two equations:

fdsfdsfdsf vdffafffy=2x+1
fdsfsdfdsfdfffafffdy=-x+5
dsf

ffMake sure that the equation is always in y=mx+b form. then you just graph it either using a calculator or slope- intercept!!!

gfFor these two equations, the graph should look like this...