Question

The tables represent two linear functions in a system.


What is the solution to this system?

(1, 0)
(1, 6)
(8, 26)
(8, –22)

Answer 1

which tables?

Answer 2

tennis :D

Answer 3

I usually use chess table(s).

Answer 4

anyway, you got anything for us, man?

Answer 5

TABLE 1 TABLE 2
\(\bbox[8pt, lightcyan ,border:8px solid black]{\LARGE \huge{ \begin{array}{| l | c | r |}
\hline \scr~~~x~~ & \scr ~~~y~~ \\
\hline
\scr~-4~ & \scr 26 \\
\hline
\scr~-2~ & \scr 18 \\
\hline
\scr~~~0~ & \scr 10 \\
\hline
\scr~~~2~ & \scr 2 \\
\hline \end{array} } ~~~~~~~ \huge{ \begin{array}{| l | c | r |}
\hline \scr~~~x~~ & \scr ~~~y~~ \\
\hline
\scr~-4~ & \scr 14 \\
\hline
\scr~-2~ & \scr 8 \\
\hline
\scr~~~0~ & \scr 2 \\
\hline
\scr~~~5~ & \scr -4 \\
\hline \end{array} } }\)

Answer 6

Can you find the slope in each table?

Answer 7

table 1 = -8/2 table 2 = -6/?

Answer 8

not negative sorry

Answer 9

oh the table 2 is written incorrectly, the last point is (2,-4)

Answer 10

ok, where are you saying it is not negative?

Answer 11

i put -8/2 and -6/2 and i put negative signs when its not decreasing.

Answer 12

oh, it surely is decreasing

Answer 13

you can see that as x is becoming a greater positive number, the y is going deeper into negative values.
And this is the case in both tables.

Answer 14

oh

Answer 15

each time x goes up by 2:

in the first table y goes down by 8.
in the second table y goes down by 6.

Therefore:

in the first table the slope is -4.
in the second table the slope is -3.

Answer 16

now, what are the y-intercepts in each of the table?
(Hint: look at the tables)

Answer 17

0,10 & 0,2

Answer 18

Yes.

Answer 19

but when you write a point, put it in parenthesis please.
Like: (0,10)

Answer 20

yeah

Answer 21

So you know that:

equation of a line (in a y intercept form, can be written as) `y=mx+b`
where m is the slope, and b is the y intercept.

you have:
table 1 table 2
slope (m) -4 -3
y-intercept (b) 10 2

what will your 2 equations be?

Answer 22

idk

Answer 23

y=mx+b
I will do the first equation for you:
y=-4x+10

Answer 24

can you do the second one for me?

Answer 25

y= -3 + 2

Answer 26

yes, almost

Answer 27

y=-3x+2, like this

Answer 28

so your two equations are
y=-4x+10
y=-3x+2

solve using substitution:
-3x+2=-4x+10

Answer 29

oh i forgot the x

Answer 30

yup... can you solve for x?

Answer 31

yeah hold for a sec so i can solve

Answer 32

sure

Answer 33

x = 8

Answer 34

yes.

Answer 35

knowing that 8 equals 8 can you solve for y?

Answer 36

that x* = 8

Answer 37

(plug in 8 instead of x into any of the 2 equations)

Answer 38

y = -22

Answer 39

yup

Answer 40

ohhh thanks man now i get it i will medal you and fan you. thank you :)

Answer 41

No need fanning, although I certainly don't mind if you do (lol).
You are one of the few questioners who has a very proper background to the subject, it is a joy to work with you. tY and yw:D

Answer 42

lol^^
btw that tables ^^O_O :O

Answer 43

nice tables aren't they (:D) ?

Answer 44

yes :( but too much work for meh
i like to use draw :P:DP