linear combinations, help please! Options

[*xcaitlinx*]

well i was absent on the day that my math class learned this concept, and my teacher expects me to "teach myself" out of the textbook over the weekend...which is impossible. it's about using linear combinations (aka "elimination method") to solve the linear system. if i give an example, could someone please explain how to solve it? thanks

directions: use linear combinations to solve the linear system.

ex: 2 - 7x = 9y
2y - 4x = 6

the only thing i figured out is that you have to switch around the equation to make it look similar--so it would be:

9y - 7x = 2
2y - 4x = 6

thanks again for the help =)

[sadolakced acid]

after you make it look similar, make one of the variables the same in both equations, like

2 *(9y - 7x = 2)
9 *(2y - 4x = 6)

that way it's

18y - 14x = 4
18y - 36x = 6

and then, you subtract them (make the second equation negative and add them)

18y - 14x = 4
-18y +36x =-6

and you get an equation of a third line, that intersects those two lines at the same point of intersection

0y + 22x = -2

22 x = -2

so you solve that and get

x= -1/11

and use that, plug it into one of the original equations

9y - 7(-1/11) = 2

and solve for y

9y + (-7)(-1/11) = 2

9y + (7/11) = 2
9y = 15/11
y = 5/33

and then you have an x and a y, so put it as an ordered pair, and you have:

(-1/11, 5/33)

hope that helped.