image

    Have a query? Ask a Tutor!!

    Access to best educators and exclusive paper discussions

    Offsite CampusTurito Championship

    Can’t find what you’re looking for?

    Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

    • Homework- One to One Solutions
    • Understand concepts to solve better
    • Get your doubts solved instantly
    Maths-
    General
    Easy

    Question

    Rewrite the equation as a system of equations, and then use a graph to solve.
    x squared minus 6 x equals 2 x minus 16

    hintHint:

    A set of equation can be solved by graphing them. Each points of intersection among the graphs are solutions for the given set. If there are no points of intersection, then there are no solutions for the set.
    We are asked to rewrite the equation into a system of equation and then use a graph to solve.

    The correct answer is: We are asked to rewrite the equation into a system of equation and then use a graph to solve.

      Step 1 of 3:
      Equate each side of the equation to a new variable, y :
      table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell y equals x squared minus 6 x space end cell row cell y equals 2 x minus 16 end cell end table
      Find three solutions of the equation, y equals x squared minus 6 x :
      When , x = 0,
      table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell y equals x squared minus 6 x end cell row cell y equals 0 minus 6 left parenthesis 0 right parenthesis end cell row cell y equals 0 space space space space space space space space space space end cell end table
      when x = -1,
      table attributes columnalign right columnspacing 0em end attributes row cell straight y equals straight x squared minus 6 straight x space space space space space space space space space space space space space space space space end cell row cell straight y equals left parenthesis negative 1 right parenthesis squared minus 6 left parenthesis negative 1 right parenthesis space space space end cell row cell straight y equals 1 plus 6 space space space space space space space space space space space space space space space space space space space end cell row cell straight y equals 7 space space space space space space space space space space space space space space space space space space space space space space space space space end cell end table space space
      when x = 1,
      table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell y equals x squared minus 6 x space space space space end cell row cell y equals left parenthesis 1 right parenthesis squared minus 6 left parenthesis 1 right parenthesis end cell row cell y equals 1 minus 6 space space space space space space space space end cell row cell y equals negative 5 space space space space space space space space space space space space end cell end table
      Thus, the solutions are, (0, 0) (-1,7)and(1, -5)
      Find two solutions of the equation y = 2x -16,
      When , x = 0,
      table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell y equals 2 x minus 16 space space space end cell row cell y equals 2 left parenthesis 0 right parenthesis minus 16 end cell row cell y equals negative 16 space space space space space space space end cell end table
      when x = 1,
      table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell y equals 2 x minus 16 space space end cell row cell y equals 2 left parenthesis 1 right parenthesis minus 16 end cell row cell y equals 2 minus 16 space space space space space space end cell row cell y equals negative 14 space space space space space space space space space end cell end table

      Thus, the solutions are (0, 0) and (1, -14)
      Step 3 of 3:
      Plot the points and join them to get the respective graph.

      Here, there is just one point where both the graphs intersect each other. The point is (4, -8). Thus, we can say that the point is the solution of the set of equation.

      When you graph a quadratic equation find three coordinate points to get the curve. But when it is a linear equation, just two points would give the path of the line.

      Related Questions to study

      General
      Maths-

      Find the simple interest on Rs. 6500 at 14% per annum for 73 days?

      Find the simple interest on Rs. 6500 at 14% per annum for 73 days?

      Maths-General
      General
      Maths-

      Rewrite the equation as a system of equations, and then use a graph to solve.
      2 x squared plus 3 x equals 2 x plus 1

      Rewrite the equation as a system of equations, and then use a graph to solve.
      2 x squared plus 3 x equals 2 x plus 1

      Maths-General
      General
      Maths-

      Rewrite the equation as a system of equations, and then use a graph to solve.
      4 x squared equals 2 x minus 5

      Rewrite the equation as a system of equations, and then use a graph to solve.
      4 x squared equals 2 x minus 5

      Maths-General
      parallel
      General
      Maths-

      Find the simple interest on Rs. 8000 at 16 % per annum for 9 months?

      Find the simple interest on Rs. 8000 at 16 % per annum for 9 months?

      Maths-General
      General
      Maths-

      The simple interest on a sum of money at the end of 5 years is  of the sum. Find the rate of interest?

      The simple interest on a sum of money at the end of 5 years is  of the sum. Find the rate of interest?

      Maths-General
      General
      Maths-

      Find the solution of the system of equations.
      y equals 2 x squared plus 5 x minus 30
      y = 2x + 5

      Find the solution of the system of equations.
      y equals 2 x squared plus 5 x minus 30
      y = 2x + 5

      Maths-General
      parallel
      General
      General

      Format the sentence into converts Spanish grammar.
      "My wife buys a new television for my father”

      Format the sentence into converts Spanish grammar.
      "My wife buys a new television for my father”

      GeneralGeneral
      General
      General

      Find the helping Verbs and Action Verbs in the following sentences.

      Find the helping Verbs and Action Verbs in the following sentences.

      GeneralGeneral
      General
      Maths-

      If Rs. 4000 amounts to Rs. 4500 in 2 years, find how much would it amount in 5 years at the same rate of interest?

      If Rs. 4000 amounts to Rs. 4500 in 2 years, find how much would it amount in 5 years at the same rate of interest?

      Maths-General
      parallel
      General
      Maths-

      Find the solution of the system of equations.
      y equals 3 x squared plus 2 x plus 1
      y equals 2 x plus 1

      Find the solution of the system of equations.
      y equals 3 x squared plus 2 x plus 1
      y equals 2 x plus 1

      Maths-General
      General
      Maths-

      Find the solution of the system of equations.
      y equals x squared plus 8 x plus 30
      y = 5 - 2x

      Find the solution of the system of equations.
      y equals x squared plus 8 x plus 30
      y = 5 - 2x

      Maths-General
      General
      Maths-

      At what rate percent per annum will a sum of money double itself in 10 years?

      At what rate percent per annum will a sum of money double itself in 10 years?

      Maths-General
      parallel
      General
      Maths-

      Find the solution of the system of equations.
      y equals x squared plus 6 x plus 9
      y = 3x

      It is not necessary for every set of equation to have solutions. If you graph them and get not intersecting points, then they have no real solutions.

      Find the solution of the system of equations.
      y equals x squared plus 6 x plus 9
      y = 3x

      Maths-General

      It is not necessary for every set of equation to have solutions. If you graph them and get not intersecting points, then they have no real solutions.

      General
      General

      Choose the synonyms of 'research'

      Choose the synonyms of 'research'

      GeneralGeneral
      General
      Maths-

      What sum will yield an interest of Rs. 277.50 for 3 years at 12% per annum?

      What sum will yield an interest of Rs. 277.50 for 3 years at 12% per annum?

      Maths-General
      parallel

      card img

      With Turito Academy.

      card img

      With Turito Foundation.

      card img

      Get an Expert Advice From Turito.

      Turito Academy

      card img

      With Turito Academy.

      Test Prep

      card img

      With Turito Foundation.