Question

Solve the system by elimination (Need to show work)
{14x-35=7y
{-25-6x=5y

Answer 1

first of all you may want to organize the variables vertically
x + y =
x + y =

then multiply one by a factor to cancel out or "eliminate" one

Answer 2

Can someone show me how to do this

Answer 3

well... firstlyi arrange your variables.. so use linear simplification to move them about

notice how they're not aligned vertically, the "x"'s should all be in one-vertical-line
same for the "y"'s

preferably on the left-hand-side \(\bf 14{\color{brown}{ x}}-35=7{\color{blue}{ y}}\\
-25-6{\color{brown}{ x}}=5{\color{blue}{ y}}\)

Answer 4

like this?
14x-35=7y
-6x-25=5y

Answer 5

well... that'd work, yes

so let us use a factor to eliminate one
one sec

Answer 6

\(\large \begin{array}{llll}
14x-35=7y&{\color{brown}{ \times -5}} &\to-70x+175=\cancel{ -35y }\\
-6x-25=5y&{\color{brown}{ \times 7}} &\to-42x-175=\cancel{ 35y }
\\\hline\\
&&\square ?\qquad +\square ?\qquad =\square ?
\end{array}\)

notice that we used -5 and 7

and notice that the multipiied version resulted in a -35y and a +35y

now add the rest vertically, see what you get

Answer 7

8x-(-60)

Answer 8

-(-60)?

Answer 9

wouldn't it be negative or no

Answer 10

you should have reduced the first equation...makes it a lot easier

Answer 11

well... youu'd be adding vertically, thus why aligning them vertically

Answer 12

so was I wrong?

Answer 13

well.... notice the addition you need to perform \(\begin{array}{llll}
14x-35=7y&{\color{brown}{ \times -5}} &\to-70x+175=\cancel{ -35y }\\
-6x-25=5y&{\color{brown}{ \times 7}} &\to-42x-175=\cancel{ 35y }
\\\hline\\
&&\square ?\qquad +\square ?\qquad =\square ?\\
&&\qquad \Uparrow\\
&&sum\ up
\end{array}\)

Answer 14

do you see how we get the 2nd set of equations?

Answer 15

well... do you see how we get the 2nd set of equations?

do you even see the 2nd set of equations ?

Answer 16

ok we multiply it by -5 and 7

Answer 17

yeap.....

and then we add vertically

Answer 18

in the addition, notice -35y+ 35y = 0 thuse they get ELIMIINATEd

Answer 19

wouldn't 175 cancel itself out because of the plus and minus sign?

Answer 20

in this case, yes, it does

so... what are you left with then \(\begin{array}{llll}
14x-35=7y&{\color{brown}{ \times -5}} &\to-70x+175=\cancel{ -35y }\\
-6x-25=5y&{\color{brown}{ \times 7}} &\to-42x-175=\cancel{ 35y }
\\\hline\\
&&\square ?\qquad +0\qquad =0
\end{array}\)

Answer 21

so -70+-42= -114x

Answer 22

well... -70-42 = -112 but yes.... then that's the equation you're left with
thus \(\bf \begin{array}{llll}
14x-35=7y&{\color{brown}{ \times -5}} &\to-70x+175=\cancel{ -35y }\\
-6x-25=5y&{\color{brown}{ \times 7}} &\to-42x-175=\cancel{ 35y }
\\\hline\\
&&-112x\qquad +0\qquad =0
\end{array}
\\ \quad \\
{\color{blue}{ -112x=0\implies x=\cfrac{0}{-112}\implies x=0}}\)

Answer 23

so now you know what "x" is

then you can plug it either equation, to get "y" by solving for "y" :)

see by multiplying like so by some factor, so that it yields the same product atop and below

one of the variables get ELIMINATED, thus the "elimination" method

Answer 24

then to get y I just put the value of x in the original equation

Answer 25

yeap

Answer 26

ok

Answer 27

weird how my book shows a more complex way

Answer 28

thanks

Answer 29

yw