Question

Which equation shows the substitution method being used to solve the system of linear equations?
x + y = 6
x = y + 5
A.(y + 5) + y = 6
B.x = (x – 6) + 5
C.x + y = y + 5
D.x + (y + 5) = 6
The system of equations is inconsistent.
What are the missing values?
5x + ___y=2
___x+3y=8
please help will fan and medal

Answer 1

if you know what a substitution method is, then you should be able to tell me.
(Hint: you are substituting "y+5" instead of x, based on our second equation)

Answer 2

(and substituting this, into the 1st equation)

Answer 3

i dont really get substitution method

Answer 4

okay, we can go through an example.
lets say you have a system below:
\(\large\color{black}{ a+b=7 }\)
\(\large\color{black}{ a=b+5 }\)

what you do is you substitute, \(\large\color{black}{ b+5 }\) instead of a, like this.

\(\large\color{black}{ \color{red}{a}+b=7 }\)
\(\large\color{black}{ \color{red}{b+2}+b=7 }\)

Answer 5

and then we are able to solve for b, right?

Answer 6

yea

Answer 7

so, in your case though, you have a different system (which is not exactly same, but very similar).

\(\large\color{black}{x + y = 6 }\)
\(\large\color{black}{ x = y + 5 }\)

based on my example, can you tell me how you susbstitute?

Answer 8

so you substitute y+5 instead of x?

Answer 9

yes

Answer 10

and which of the options will this substitution give us?

Answer 11

A?

Answer 12

yes, there you go!

Answer 13

yay! lol and could you help me with the second one?

Answer 14

surely...

Answer 15

The system of equations is inconsistent.
What are the missing values?
5x + ___y=2
___x+3y=8

Answer 16

i didnt really get this one

Answer 17

I am thinking that you just have to find the value of x and the value of y, which would make the 2 equations into parallel lines (but should not be the same exact line).

Answer 18

connection again...

Answer 19

typically, something like this,
(where a, b, c, and d, are just numbers.)

\(\LARGE\color{black}{ \color{red}{a}~x+\color{blue}{b}~y=\color{darkgoldenrod}{c} }\)
\(\LARGE\color{black}{\color{red}{a}~x+\color{blue}{b}~y=\color{green}{d} }\)

(and in both equations a and b are same number, but c does not equal d)

Answer 20

in your case you have:

\(\LARGE\color{black}{ \color{red}{5}~x+\color{blue}{?_{_2}}~y=\color{darkgoldenrod}{2} }\)
\(\LARGE\color{black}{\color{red}{?_{_1}}~x+\color{blue}{3}~y=\color{green}{8} }\)

Answer 21

(by \(\LARGE\color{black}{ \color{blue}{?_{_2}} }\) I mean the second question,
and by \(\LARGE\color{black}{\color{red}{?_{_1}} }\) I mean th first question)

Answer 22

im still confused

Answer 23

you need to set your system in a format of
\(\LARGE\color{black}{ \color{red}{a}~x+\color{blue}{b}~y=\color{darkgoldenrod}{c} }\)
\(\LARGE\color{black}{\color{red}{a}~x+\color{blue}{b}~y=\color{green}{d} }\)

Answer 24

you know from the first equation, that a=5, and c=2,
and from the second equation that b=3 and d=8

Answer 25

still confused, or need time to process?

Answer 26

yea im like lost

Answer 27

okay, do you see that in your case, the blank next to x in the second equation, and 5 next to x in a 1st equation should be the same number?

Answer 28

yes

Answer 29

so it shoud be 5x+3y and in the second one it would be the same thing?

Answer 30

yes

Answer 31

So you have: \(\LARGE\color{black}{ \color{red}{5}~x+\color{blue}{3}~y=\color{darkgoldenrod}{2} }\)
\(\LARGE\color{black}{\color{red}{5}~x+\color{blue}{3}~y=\color{green}{8} }\)

Answer 32

thanks for your help..again lol

Answer 33

if you subtract the 2 equations the left side is going to be zero, and the right is -6, and you know that
0 doesn't equal to -6.

there is the inconsistency.

Answer 34

yw