Question

Use the Substitution Method to solve the following system of equations.
x - 4y = 1
2x - 9y = 3

(-1, -3)
(-3, 1)
(3, 1)
(-3, -1)

Answer 1

you can use any method you like, including checking the answers to see which one works

Answer 2

Alright, so, do you know the first step?

Answer 3

this must be a different problem right?

Answer 4

Uh...Those aren't even the equations you're using.
x - 4y = 1
2x - 9y = 3
First, choose a variable. Either y or x

Answer 5

oops sorry.

Answer 6

what problem do you need to solve? is it this one
\[x - 4y = 1\]\[ 2x - 9y = 3\]

Answer 7

yes

Answer 8

you can solve the first equation for \(x\) via \(x=4y+1\) and then substitute it in to the second equation to get
\[2(4y+1)-9y=3\]

Answer 9

\[x-4y=1 <=> y=x/4 -1/4\]
put y into the second equation
\[2x - 9y = 2x - 9(x/4 - 1/4) = 3 <=> x=-3\]
thus
\[y=x/4 -1/4 = -1\]

Answer 10

then solve that one in a couple of steps
multiply out to get
\[8y+2-9y=3\] combine like terms to get
\[-y+2=3\] subtract 2 get \[-y=1\] so \[y=-1\]

Answer 11

so the first part is -1 ?

Answer 12

it is \(y=-1\) then you can solve for \(x\)

Answer 13

or, since you have only one choice with the second number as \(-1\) you can assume that it is the choice \((-3,-1)\)

Answer 14

no :/ the teacher cant really explain this too good

Answer 15

u jus said the first part would be -1
so how would it be second ?

Answer 16

That's the y.
(x, y)

Answer 17

@mikaa_toxica13 i solved for \(y\) not for \(x\)
\(y\) is the second coordinate, not the first coordinate

Answer 18

oh okay i see

Answer 19

sorry i got confused

Answer 20

now that you know \\(y=-1\) and you know \(x - 4y = 1\) that means
\[x-4(-1)=1\] so
\[x+4=1\iff x=-3\]

Answer 21

first coordinate is \(-3\) and the second is \(-1\)

Answer 22

okay thank u soo much !!