Question

which ordered pair is the solution to the system of equations below?
x+3y=7
x+2y=10

Answer 1

(16,-3) is the ordered pair of these equations

Answer 2

can you explain how you got that please?

Answer 3

I would use substitution.

Answer 4

7-3y=x so 7-3y+2y=10

Answer 5

7-y=10

Answer 6

-3=y

Answer 7

x+3(-3)=7

Answer 8

x=-2

Answer 9

i solved by multiplying both equations by 3and first i got y value and substitute y vale in any equaton u will get x value

Answer 10

You would multiply them both by 1/3

Answer 11

... not 3.

Answer 12

the eqtns r in the form when u multi[ly by 3 on both sides
3x+9y=21
3x+6y=30
now subtract both equations then u will get 3y=-9 then y=-3
substitute y=-3 in any equation u get 16

Answer 13

multiplying 3 is correct@lord

Answer 14

hope the answer is done

Answer 15

.so by multiplying by three the goal is to get rid of one of the variables right?

Answer 16

yes

Answer 17

and u always subtract the equations?

Answer 18

when u get 1 value it will b easy to find other

Answer 19

okay thanks alot.. i understand now :)

Answer 20

its way of saying thnks :)

Answer 21

you can save a step by multiplying one of them by -3 instead, that preps it for subracting

Answer 22

u can do anyway yaar

Answer 23

im not sure why the use of 3, did i read something in the post wrong?

Answer 24

3 and -3 work fine, a little redundant, but fine

ida gone with multiplying the second by -1

Answer 25

x+3y=7
x+2y=10 ; *-1


x+3y = 7
-x -2y =-10 ; now combine
-----------
y = -3

Answer 26

nyhow u can do

Answer 27

soo if you multiply the bottom by a -1 then u dont have to multiply the top one by -1?

Answer 28

not required

Answer 29

systems of equations have the property that scaling an equation doesnt change the variables outcomes

Answer 30

the multiplying is just to change the form so that you can combine them to easily eliminate one of the variables from the process

Answer 31

oh okay

Answer 32

i simple example is of that property is:

y = x has the same solutions as 2y=2x or y/3=x/3, or ny=nx

Answer 33

okay so how do you know if the lines are parallel, or intersecting? does this apply to this type of problem or no?

Answer 34

if one eqaution is a scalar of the other, they are the same line

if one equation is almost a scalar of the other, and they differ only by a constant, they are parallel

Answer 35

for example

x+y = 3 , we can scale this by any factor and its still the same line

2x+2y = 6, or -5x-5y=-15 the line itself is not changing

Answer 36

but, if they differ by only the constant term they are not the same line, but run in the same direction

x+y = 3
2x+2y=3

would be parallel

Answer 37

if they dont meet either of these criteria, the lines will intersect at some point

Answer 38

so wouldnt this be identicle? or would it be parallel?

y=-2+3
5y=-10x+15

Answer 39

lets test it out, multiply the top by 5

Answer 40

and your missing the "x" but i assume that a stypo :)

Answer 41

oh yes its -2x
sorry

Answer 42

(y=-2x+3) *5
5y=-10x+15

5y= -10x+15
5y=-10x+15

same is same is same

Answer 43

when lines are the same, they are called "coinciding" parallel refers to separate lines

Answer 44

okay! sorry im asking soo many questions i just want to understand :) thanks alot!

Answer 45

understanding is good ;)

Answer 46

haha yeah