Question

Last One I'll Give Medal If I Get This One Right..
What is the solution to the system?
Line 1
x y
-2 -4
-1 -1
Line 2
x y
2 3
3 1

(____,____)

Answer 1

I think its \[3 and 2 \]

Answer 2

Nope

Answer 3

How did you get it ?

Answer 4

i divided 1-10 and 4-(-2)

Answer 5

and got \[\frac{ 9 }{ 6 }\]

Answer 6

and

Answer 7

and why did you divide them in the very beginning ?

Answer 8

2-(-2) and 1-(-1) and got \[\frac{ 4 }{ 2}\]

Answer 9

because i got them down from the chart and divided

Answer 10

See:

A solution to a system basically means that it should satisfy all the equations in that system

Answer 11

Right ?

Answer 12

Right

Answer 13

Good. So, this means that whatever point you get as the answer should lie on both the lines Line 1 and line 2. Ok ?

Answer 14

ok

Answer 15

So, if I could find out the equations of both the lines - line 1 and line 2, I could solve them to get the answer

Answer 16

So, my task is to find out the equation of a line using two given points.

Answer 17

Lets see how we can do it...

Let I have a line say line - 3 and have 2 points , say (1,2) and (4,5) which lie on this line.

Answer 18

they'd be inconsistent

Answer 19

Its just an example :)

Answer 20

oh.

Answer 21

:)

Answer 22

:)

Now, lets see...

An equation of a line is :

y = mx + c

Answer 23

Now, since (1,2) and (4,5) lie on line 3 so they must satisfy the equation y = mx + c.

Right ?

Answer 24

Ya

Answer 25

So... lets plug-in the values:

2 = m * 1 + c ------- (1)

5 = m * 4 + c ------- (2)

Now can you solve these 2 equations to get 'm' and 'c' ?

And if you have any doubt... don't forget to ask :)

Answer 26

Give it a try... I will wait

Answer 27

k thanx

Answer 28

No problem.. :)

Answer 29

please, you have to determine the equations of your lines, first, using the points that you are provided

Answer 30

that explanation :)
and alexi you can also use same method like we did for previous questions
find slope of both tables (you are really good in it you can find that easily)
then find equation y-intercept then you can graph or use other method to find solution
up to u :)

Answer 31

good explanation**

Answer 32

@Michele_Laino is right... Once you have calculated m and c, then you can use the same method to find out the equations of line 1 and line 2... Then solve them and *VOILA* ... there's your answer

@Nnesha thanks :)

Best of luck!

Answer 33

There is another way... if you like... and that is by plotting the graphs...

Answer 34

For example:

line 3's graph would be something like:



Similarly you can draw line 1 and line 2 and where they intersect- that is your required point

Answer 35

k i finished is it (2,7)?

Answer 36

2,7 ... uhm are these the values of m and c ? or the answer to your original question ?

Answer 37

...yea...

Answer 38

m and c ??

In that case, sorry its wrong..

Answer 39

Let me explain...

Answer 40

2 = m * 1 + c ------- (1)

5 = m * 4 + c ------- (2)

So, if I subtract equation (1) from equation (2), what would I get

Answer 41

Any doubt ?

Answer 42

Take your time... and tell me if you have any doubt

Answer 43

What?

Answer 44

Let me be more clear...

I just chose some random line say line 3 and 2 points lying on it (1,2) and (4,5)... This line and these points are not from your question ... its just to get you some idea...

Answer 45

-.- okai.

Answer 46

Then, we substituted those points in our equation of line 3 (which I assumed was y = mx +c) and thus got 2 equations:

5 = 4m + c by putting x = 4 and y = 5

and

2 = m + c by putting x = 1 and y = 2

Answer 47

Clear ?

Answer 48

ya

Answer 49

Great !

Now, I used these 2 equations to get the values of m and c, so that I can get the equation of line 3 (which will not have the stuff like m and c but some numbers in place of them)

Answer 50

Now, how did I solve those 2 equations :

I subtracted the 2 equations (like I have showed in the image).

I got:

\[\large{3m = 3}\]

\[\large{\implies m= \cfrac{3}{3} = 1}\]

Any problem ?

Answer 51

no

Answer 52

Good...

Now, I have the value of m, so lets see how I can get 'c' :

I had :

2 = m + c

Now, I put m = 1, I get :

2 = 1 + c

=> c = 1

Any doubt ?

Answer 53

no

Answer 54

So, our equation of line 3 is:

y = mx + c

Put m =1 and c = 1

y = x + 1

Now just as I calculated the equation of line 3, try calculating the equation of line 1...

Answer 55

Line 1
x y
-2 -4
-1 -1

(from your question)

2 points which lie on the line are (-2, -4) and (-1, -1)... see if you can find out the equation...

Follow the same method which I used above step by step and tell me if you have any doubt