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A pair of equations is shown below: y = 3x - 5 y = 6x - 8

Part A: Explain how you will solve the pair of equations by substitution or elimination. Show all the steps and write the solution. (5 points)

Part B: If the two equations are graphed, at what point will the lines representing the two equations intersect? Explain your answer. (5 points) ​

Respuesta :

Answer:

See below

Step-by-step explanation:

y = 3x -5     <===== multiply this equation by -2 to get

-2y = -6x+10    now add it to the other equation(this will ELIMINATE x)

  y = 6x-8  

-y  = +2

y = -2       then sub this in to oneof the quations to find x = 1

the two points will intersect at x,y = 1,-2    (because this satisfies both of the equations)

KennyOliver

PART A

We start with:  y = 3x - 5  y = 6x - 8

Elimination:

  • If we have two equations that  = y, then we can make them equal each other:
  • y = y
  • 3x - 5 = 6x - 8
  • We then collect the x term together:
  • 3x - 6x = -8 + 5
  • -3x = -3
  • We can divide both sides by -3:
  • x = 1

Substitution

  • We can make one equation turn from a y= to an x=
  • I decided to go with y = 3x - 5 (but it doesn't matter)
  • We basically want to get it into x=
  • y = 3x - 5
  • y + 5 = 3x
  • 3x = y + 5 (I'm just flipping the equation to get x on the left for easiness)
  • We then divide both sides by 3:
  • x = [tex]\frac{y + 5}{3}[/tex]
  • Don't forget we've also got y = 6x - 8
  • So we just put x in!
  • y = 6 × [tex]\frac{y + 5}{3}[/tex] - 8
  • y = [tex]\frac{6}{3}[/tex] × (y + 5) - 8
  • y = 2 × (y + 5) - 8
  • y = 2y + 10 - 8
  • y = 2y + 2
  • Rearrange to get y on one side:
  • -y = 2
  • Times both sides by -1:
  • y = -2
  • We can now go back to...
  • x = [tex]\frac{y + 5}{3}[/tex]
  • By putting y = -2 in:
  • x = [tex]\frac{-2 + 5}{3}[/tex]
  • x = [tex]\frac{3}{3}[/tex] = 1

PART B

  • We can find where they intersect/overlap by using elimination/substiution
  • We've already covered both, and we get x = 1
  • This means we've already go the x-coordinate of our point where the lines meet
  • (x, y) = (1, ?)
  • We just put our value of x into either equation (since x = 1 is where they meet)
  • I'll go with y = 6x - 8
  • y = 6 × 1 - 8
  • y = 6 - 8 = -2
  • We end up with (1, -2)!!!

P.S.:

I've attached a screenshot of the graphs, notice how they meet at (1, -2)

Ver imagen KennyOliver

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