Question

What is the solution of the following system?
-2x-y=0
3x-y=10
possible answers are:
1. infinitely many solutions
2. no solutions
3. (3,8)
4. (-3,-8)

Answer 1

recheck your equations, are there any missing negative signs somewhere, or some other value missing?

Answer 2

I checked its not missing anything @jdoe0001

Answer 3

well... if you solve the 1st equation for "y", what would you get?

Answer 4

y=2x? @jdoe0001

Answer 5

well... -2x -y + y = 0 + y => -2x = y

Answer 6

so now we know that y = -2x
so let us use that in the 2nd equation then \(\bf y = -2x\qquad thus\\ \quad \\
3x-y=10\implies 3x-(-2x)=10\implies 3x+2x=10\implies 5x=10\\ \quad \\\implies x =2\\ \quad \\
\textit{using our new found "x" in say the 1st equation, we get}\\ \quad \\
-2x-y = 0\implies -2(2)-y=0\implies -4 = y
\)

Answer 7

so as you can see, x = 2, y = -4 so the solution will be ( 2 , -4 )

and is not one of your choices

Answer 8

well now I don't know what to do because those are my only choices lol oh well. could you help me with a different one? @jdoe0001

Answer 9

ok

Answer 10

Solve the system by substitution.
-4.5x-2y=-12.5
3.25x-y=-0.75
I have to show work step by step but I have no idea how to even start it

Answer 11

@jdoe0001

Answer 12

same thing, you'd solve either equation for "y"

once you get "y", you use that equivalent in the other equation by SUBSTITUTING the "y'" there

Answer 13

that's all I did, you solved for "y" on the 1st one, and I used that "y" equivalent in the 2nd one

Answer 14

could you help me with solving for y on the first equation and then ill do the second one myself because I think im soling for y incorrectly @jdoe0001

Answer 15

okie dokie
\(\bf -4.5x-2y=-12.5\qquad \textit{adding 12.5 to both sides}\\ \quad \\
-4.5x-2y+12.5=\cancel{-12.5+12.5}\implies -4.5x-2y+12.5=0\ \quad \\\qquad \textit{adding 2y now}\\ \quad \\
-4.5x\cancel{-2y+2y}+12.5=0+2y\implies -4.5x+12.5=2y\ \quad \\\qquad \textit{dividing by 2}\\ \quad \\
\cfrac{-4.5x+12.5}{2}=\cfrac{\cancel{2}y}{\cancel{2}}\implies \cfrac{-4.5x+12.5}{2}=y\)

Answer 16

so y in that eqaution= 2.25+6.25? @jdoe0001

Answer 17

-2.25x + 6.25 <--- yes

Answer 18

which is 4 right so I sub 4 in for y in the second equation?

Answer 19

@jdoe0001

Answer 20

4? what do you mean? y = 4?

Answer 21

yeah 6.25-2.25 is 4? @jdoe0001

Answer 22

\(\Large -2.25\color{red}{x} + 6.25 = y\)

Answer 23

so 3.25x-2.25x+6.25=-0.75 for the second equation

Answer 24

@jdoe0001

Answer 25

well, kinda, recall that - times - = +
and that - times + = -

same sign multiplication gives use POSITIVE
different sign multiplication gives use NEGATIVE

\(\bf 3.25x-y=-0.75\implies 3.25x-(-2.25x + 6.25)=-0.75\\ \quad \\
\color{blue}{-(-2.25x + 6.25)\implies +2.25x-6.25}\qquad thus\\ \quad \\
3.25x-(-2.25x + 6.25)=-0.75\implies 3.25x+2.25x-6.25=-0.75\)

Answer 26

oh okay thanks! @jdoe0001

Answer 27

yw