intersecting lines using elimination method (take two)?

Question

my professor used "the elimination method" to find the intersection of these lines. i didn't pay attention (It was an operations management course) but now i figure it will help me save time on the exam. can someone set this up for me and get the intersection of the line. i already know the answer (10,10) but not how he got it. if i don't get this, i'll have to use the long, drawn out formula.

line 1: 2x + y = 30
line 2: 2y + 2x = 30

Thanks for your help!

I ASKED THIS QUESTION EARLIER AND YOU GUYS POINTED OUT THAT THE LINES WERE PARALLEL. HERE ARE THE RIGHT ONES SO HOPEFULLY I CAN GET SOME HELP THIS TIME!

damnit! i typed it in wrong again. thats what i get for not paying attention. the equations are: 2x + y = 30 and 2y + x = 30. thanks anyway guys!!!

Answer 1

OK, now you wrote things in a correct way

Multiply the second equation by -1

2x + y = 30
-2x - 2y = -30

Add

You wont have x anymore, then you will be able to calculate the y value.

Finally plug it in one of the equations and get x

Ana

Answer 2

Rearranged equations to

2x + y = 30
2x +2y=30 Multiply first equation by -1 and add it to second.

2x + 2y = 30
-2x - y = -30
0 +y = 0
x = 15 and y = 0 The lines have in common the point (15,0)

your answer (10, 10) does not satisfies the equation

2(10) + 2 (10) ≠ 30

Answer 3

Check your equations. If x is 10 and y is 10 too, then 2x + y = 30 but 2x + 2y is 40

I think that you were meaning this

2x + y = 30
x + 2y = 30

Then do this:

Multiply the second one by -2, then just add and do as I explained you before

Ana

Answer 4

Something isn't right here.

You have 2x + y = 30
and 2y +2x = 30.

So, I should be able to equate them:

2x +y = 2x + 2y

So we can subtract 2x from each side:

y = 2y

y = 0 , x = 15. Either you've typed in the question wrong, or you have made a mistake.

Answer 5

the ans(10,10) is wrong....it satisfies line 1 but not line 2..check it out....

see my elemination method.....can u get it .....it is similar for all two line equations....

rearrange line 2 in x,y = number ...ok
then line1: 2x+ y = 30
and line 2: 2x + 2y = 30
subtract the two lines, then u'l get
-y = 0
(i.e) y = 0
substitute y = 0 in anyone of the lines.
2x + 0= 30
2x = 30
x = 15
therefore x = 15,y=0
if u want to check :
line 1: 2(15) +0 = 30......ok..then
line 2: 2(0) +2(15) = 30...ok..it satisfies both line equation.

Answer 6

2x + y = 30 multiply by -2
-4x-2y=-60
2y + x = 30
x+2y=30
-4x-2y=-60 add
-3x=-30 dividy by -3
x=10
substitute
2x + y = 30
20+y=30 subtract 20
y=10
(10, 10)

check
2y + x = 30
20+10=30

Answer 7

2x + y = 30 - line 1
x + 2y = 30 - line 2

multiply -2 to line 2

2x + y = 30
-2x - 4y = -60
___________
- 3y = -30
y = 10

substitute y=10 to line 1

2x + y = 30
2x + 10 = 30
2x = 30-10
2x = 20
x = 10

Solution set: (10, 10)