anonymous
  • anonymous
Choose the equivalent system of linear equations that will produce the same solution as the one given below. 4x - y = -11 2x + 3y = 5
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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Zale101
  • Zale101
Have you solved systems of linear equations before? If so, do you have any ideas of where to start?
anonymous
  • anonymous
no i have idea
anonymous
  • anonymous
no idea**

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Zale101
  • Zale101
4x - y = -11 2x + 3y = 5 Here's the steps to these kind of questions. Step 1: Choose one of the equation above and solve for one variable x or y (depends on your choice) Step 2: After you solve for, let's say X, you plug whatever you got for x into the second equation that you didn't began with. Step 3: When you plug in what you solved for x into the second equation, all the variables will become y. You solve for y, and you'll get a number. Plug that number to either one of the equations and see what you'll get for x. If none of that seems familiar with you, then i will do my best to help and make you understand this.
Zale101
  • Zale101
Step 1: Which equation are you choosing from: ? 4x - y = -11 2x + 3y = 5
anonymous
  • anonymous
does it matter which one i choose
Zale101
  • Zale101
Nope. It does not matter.
Zale101
  • Zale101
Which equation is the easiest to solve for y?
Zale101
  • Zale101
I'd go with the easiest and i'll choose the first equation.
anonymous
  • anonymous
2x+3y=5 there is no negatives so its probably easier to solve
Zale101
  • Zale101
Okay, we'll go with that.
anonymous
  • anonymous
oops lol we can go with yours
Zale101
  • Zale101
Okay.
Zale101
  • Zale101
i'll choose the variable y because it's alone by itself. We can get rid of negatives when we divide both sides by negative :)
Zale101
  • Zale101
\(\large 4x - y = -11 \) Subtract both sides by 4x \(\large 4x-4x - y = -11-4x \) \(\large - y = -11-4x \) Divide both sides by -1 \(\Large \frac{- y}{-1} = \frac{-11-4x}{-1} \) \(\large y = 11+4x \)
Zale101
  • Zale101
Makes sense?
Zale101
  • Zale101
what is y equal to now?
anonymous
  • anonymous
14x ? im sorry im so confused on this, and my teacher isnt responding
Zale101
  • Zale101
Why 14 x? We can't add 11 with 4x because they are different terms. Y is equal to 11+4x, that's the only info we know
anonymous
  • anonymous
idk what to do
Zale101
  • Zale101
What does step 2 say?
anonymous
  • anonymous
After you solve for, let's say X, you plug whatever you got for x into the second equation that you didn't began with.
Zale101
  • Zale101
Yes. But let's not deal with x since we are dealing with y. So, in different wording, we take whatever we got for y and plug it for the y in the second equation. Makes sense?
Zale101
  • Zale101
y=11+4x Our second equation is 2x+3y=5 \(\large 2x+3(11+4x)=5 \)
anonymous
  • anonymous
2x+33+12x=5 ? or do you not use distributive property
Zale101
  • Zale101
Yes, you already distributed it
Vocaloid
  • Vocaloid
yup, you're right so far, now let's keep going right now we have: 2x+33+12x=5 now add the x's together: 2x + 12x = __x fill in the blank
anonymous
  • anonymous
how do i solve that? add or multiply?
anonymous
  • anonymous
so 14x
anonymous
  • anonymous
oh yeah sorry
Vocaloid
  • Vocaloid
yes, so now we have 14x + 33 = 5 subtract 33 from each sign
Vocaloid
  • Vocaloid
*from each side
anonymous
  • anonymous
-19=-28
anonymous
  • anonymous
am i supposed to subtract 33 from 33 too or no
Vocaloid
  • Vocaloid
not quite, remember that you can't combine variables and numbers 14x + 33 - 33 = 14x 5 - 33 = -28 14x = -28, make sense so far?
anonymous
  • anonymous
yes
Vocaloid
  • Vocaloid
14x = -28 divide both sides by 14
anonymous
  • anonymous
x=-2
Vocaloid
  • Vocaloid
good, we're almost done we know that x = -2 now, so we can find y let's go back to our first equation: 4x - y = -11 can you tell me what y is now?
anonymous
  • anonymous
-2
Vocaloid
  • Vocaloid
not quite. let's try plugging in -2 into the equation 4*(-2) - y = -11 -8 - y = -11 now can you tell me what y is?
anonymous
  • anonymous
no i dont understand
Vocaloid
  • Vocaloid
-8 - y = -11 add 8 to both sides, what do you get?
anonymous
  • anonymous
-y=-19
Vocaloid
  • Vocaloid
add, not subtract -11 + 8 = ?
anonymous
  • anonymous
-3
Vocaloid
  • Vocaloid
right, so -y = -3 what is y?
anonymous
  • anonymous
3
Vocaloid
  • Vocaloid
boom, we're done x = -2 and y = 3 our solution is (-2,3)
anonymous
  • anonymous
thanks
anonymous
  • anonymous
Solve the system of equations by substitution. What is the solution for x? 2x + y = 1 4x + 2y = -2 can you help with this one too?

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