Question

Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this.
2x + 10y = 58
-14x + 8y = 140

Answer 1

hey @RenaeMonroe . do you have any idea about elimination method?

Answer 2

well i think i just divide by 2 but not sure

Answer 3

Ok, I'll explain you

Answer 4

We have two equations
\[2x + 10y = 58 \]\[-14x + 8y = 140 \]
Here we'd eliminate one of the variables either x or y by adding or subtracting the two equations
let's see
which one is easy to eliminate.
if I choose y,
coefficients of y in the two equations
10 and 8
so I'll multiply the first equation by 4 and second equation by 5
\[4\times(2x+10y)=58 \times 4=>8x+40=232\]
\[5\times(-14x + 8y )= 140\times 5 =>-70x+40y=700\]
so the coefficients of y in both will become 40
do you get this part?

Answer 5

yes

Answer 6

Now we'll subtract the two equations, y will get eliminated and then we could find x. Then we'll plugin the value of x in any of the original equations to find y.
Do you understand this?

Answer 7

8x+40y=232
- -70x+40y=700
------------------
-78+y=468

Answer 8

do you get this?

Answer 9

yes

Answer 10

2(-6)+10y=58

Answer 11

-12+10y=58
10y=58-12
10y=46
divide 46/10=4.6 so y = 4.6
is this right

Answer 12

a small mistake
\[-12+10y=58\]
Add 12 to both the sides
\[-12+12+10y=58+12\]
\[10y=70\]

Answer 13

ok ic so y = 7

Answer 14

@RenaeMonroe did you understand the way?

Answer 15

yes i just forgot about that step

Answer 16

ok, now would you try to solve this problem eliminating x ?

Answer 17

14(2x+10y)58*14=>28x+140y=812
2(-14x+8y)=140*2=>-28x+16y=280

28x+140y=812
+(-28x)+16y=280
=156y=1092
y=7

Answer 18

very good but there's a short way here
multiply first by 7 and then just add it to the second
\[14x+70y=406\]
\[-14x+8y=140\]
\[78y=546\]

Answer 19

oh k thanks

Answer 20

welcome :D

Answer 21

thanks for the medal to

Answer 22

:D

Answer 23

i have a few more questions to get answers for.

Answer 24

close this and post them one by one :)

Answer 25

ohk thanks