anonymous
  • anonymous
Solve the following system of equations: x − 2y = 6 2x − 4y = 10
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
do you move the x to the other side first or do you just solve
karatechopper
  • karatechopper
Well have you heard of substitution or elimination?
anonymous
  • anonymous
yes

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karatechopper
  • karatechopper
Which process do you prefer?
anonymous
  • anonymous
substitution
anonymous
  • anonymous
so the equation would look like this 2y=x-6
karatechopper
  • karatechopper
What variable do you want to use?
anonymous
  • anonymous
x and y
karatechopper
  • karatechopper
Okay pick one. :)
anonymous
  • anonymous
x-2y=6
karatechopper
  • karatechopper
Lol tyler. I'm asking you to pick a variable that we can solve for in order to substitute.
anonymous
  • anonymous
oh lol x
karatechopper
  • karatechopper
ahah alrighty then.
karatechopper
  • karatechopper
x − 2y = 6 Solve that equation for x now. :)
anonymous
  • anonymous
so you would substitute 0 for x and the equation (0)-2y=6
karatechopper
  • karatechopper
nooooooooooooo
karatechopper
  • karatechopper
where have you go that my friend
karatechopper
  • karatechopper
Solve for x :)
anonymous
  • anonymous
oops
anonymous
  • anonymous
x-2(0)=6
anonymous
  • anonymous
x=6
karatechopper
  • karatechopper
.uhm. We need to isolate x x − 2y = 6 Add 2y to both sides in order to make x be on its own. Whats x= now?
anonymous
  • anonymous
x=2y+6
karatechopper
  • karatechopper
YAY! :D
karatechopper
  • karatechopper
Okay now let's look at the second equation.
karatechopper
  • karatechopper
2x − 4y = 10
anonymous
  • anonymous
ok
karatechopper
  • karatechopper
We know that x=2y+6 Now plug that value for x into this equation 2x − 4y = 10
anonymous
  • anonymous
ok so 2(2y+6)-4y=10
anonymous
  • anonymous
4y+12-4y=10
anonymous
  • anonymous
8y+12=10 8y=-2
karatechopper
  • karatechopper
Wait a minute..
karatechopper
  • karatechopper
2(2y+6)-4y=10 4y+12-4y=10 4y-4y=0 12=10 Dang we did something wrong.
anonymous
  • anonymous
yeah maybe we entered the wrong equation
karatechopper
  • karatechopper
uhm lets try solving for x in the bottom equation? 2x-4y=10
karatechopper
  • karatechopper
actually don't...it won't work again.
karatechopper
  • karatechopper
Are you okay if we try elimination?
anonymous
  • anonymous
yeah sure
karatechopper
  • karatechopper
Yay. x − 2y = 6 2x − 4y = 10 Okay so let's try to eliminate x, we will multiply the top equation by -2, Could you do that for me please?
anonymous
  • anonymous
yay
anonymous
  • anonymous
you multiply everthing by two or what
karatechopper
  • karatechopper
yes by -2
anonymous
  • anonymous
ok so -2x-(-4)y=-20
karatechopper
  • karatechopper
what is 6 x -2?
karatechopper
  • karatechopper
We just wanted to multiply x-2y=6 You should have gotten (-2)x-(-2)(2)y=6(-2)
anonymous
  • anonymous
-2x-(-4)y=-12
karatechopper
  • karatechopper
okay what is a negative times a negative
anonymous
  • anonymous
positive
anonymous
  • anonymous
so its a positive 4y
karatechopper
  • karatechopper
yes
karatechopper
  • karatechopper
now rewrite the equation we have.
anonymous
  • anonymous
-2x+4y=-12
karatechopper
  • karatechopper
Alright turn up.
anonymous
  • anonymous
yay
karatechopper
  • karatechopper
So lets rewrite the whole thing. -2x+4y=-12 2x − 4y = 10 Now, solve it out. As you can see...both variables cancel out... Did you post the right question? Also, the answer because we cannot solve it is.... No solution.
anonymous
  • anonymous
? Show that the solution to the system of equations 10x + y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations Show that the solution to the system of equations 10x − 2y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations Show that the solution to the system of equations 11x − y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations Show that the solution to the system of equations 11x + y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations
karatechopper
  • karatechopper
Woah there amigo, what is this?
anonymous
  • anonymous
the answers
karatechopper
  • karatechopper
What? Those look like dif questions, I am confused.
anonymous
  • anonymous
ok look at this
anonymous
  • anonymous
A system of equations is shown below: 6x − 2y = 3 (equation 1) 5x + 3y = 4 (equation 2) A student wants to prove that if equation 2 is kept unchanged and equation 1 is replaced with the sum of equation 1 and a multiple of equation 2, the solution to the new system of equations is the same as the solution to the original system of equations. If equation 2 is multiplied by 1, which of the following steps should the student use for the proof? Show that the solution to the system of equations 10x + y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations Show that the solution to the system of equations 10x − 2y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations Show that the solution to the system of equations 11x − y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations Show that the solution to the system of equations 11x + y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations
anonymous
  • anonymous
thats the whole question
karatechopper
  • karatechopper
@TheSmartOne Will try to help you for a bit, I've got to finish something else. Hope I was some sort of help. Sorry.
anonymous
  • anonymous
your fine you were help @karatechopper
TheSmartOne
  • TheSmartOne
which question are we working on?
anonymous
  • anonymous
the one up above
anonymous
  • anonymous
but ill show you it just in case you didnt see it
anonymous
  • anonymous
A system of equations is shown below: 6x − 2y = 3 (equation 1) 5x + 3y = 4 (equation 2) A student wants to prove that if equation 2 is kept unchanged and equation 1 is replaced with the sum of equation 1 and a multiple of equation 2, the solution to the new system of equations is the same as the solution to the original system of equations. If equation 2 is multiplied by 1, which of the following steps should the student use for the proof? Show that the solution to the system of equations 10x + y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations Show that the solution to the system of equations 10x − 2y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations Show that the solution to the system of equations 11x − y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations Show that the solution to the system of equations 11x + y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations
TheSmartOne
  • TheSmartOne
It's an interesting problem, hmmmm.
TheSmartOne
  • TheSmartOne
can you add these 2 equations and tell me what you get: 6x − 2y = 3 5x + 3y = 4
anonymous
  • anonymous
ok
TheSmartOne
  • TheSmartOne
so basically, what is 6x + 5x -2y + 3y = 3 + 4
anonymous
  • anonymous
yeah sorry i was doing something else
anonymous
  • anonymous
11x-y=7
TheSmartOne
  • TheSmartOne
and which answer choice has 11x-y=7 ?
anonymous
  • anonymous
the third and the fourth one
anonymous
  • anonymous
C and D
TheSmartOne
  • TheSmartOne
C has 11x \(\bf\color{red}{−}\) y = 7 D has 11x \(\bf \color{red}{+}\) y = 7
anonymous
  • anonymous
so the answer is C
anonymous
  • anonymous
@TheSmartOne
TheSmartOne
  • TheSmartOne
correct
anonymous
  • anonymous
awesome thank you
TheSmartOne
  • TheSmartOne
np :)

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