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.

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