Maths-
General
Easy

Question

What does the graph of the system of equations tell you about its solutions?
y equals 3 x squared minus 4 x plus 2
y equals 8 x minus 10

hintHint:

A graph is a geometrical representation of an expression. It can be used to solve an equation as well.
We are asked to explain what the graph of the set of equation tells about the solutions.

The correct answer is: We are asked to explain what the graph of the set of equation tells about the solutions.


    Hint:
    A graph is a geometrical representation of an expression. It can be used to solve an equation as well.
    We are asked to explain what the graph of the set of equation tells about the solutions.
    Step 1 of 3:
    Find three set of coordinate points corresponding to y equals 3 x squared minus 4 x plus 2.
    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 3 x squared minus 4 x plus 2 space end cell row cell y equals 0 minus 0 plus 2 space space space space space space space end cell row cell y equals 2 space space space space space space space space space space space space 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 3 x squared minus 4 x plus 2 space space space space space space space space space space space space space end cell row cell y equals 3 left parenthesis negative 1 right parenthesis squared minus 4 left parenthesis negative 1 right parenthesis plus 2 end cell row cell space y equals 3 left parenthesis 1 right parenthesis plus 4 plus 2 space space space space space space space space space space space space space space space end cell row cell space y equals 3 plus 4 plus 2 space space space space space space space space space space space space space space space space space space space space end cell row cell y equals 9 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 space space space space space space space end cell end table 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 3 x squared minus 4 x plus 2 space space space space space space space space end cell row cell y equals 3 left parenthesis 1 right parenthesis squared minus 4 left parenthesis 1 right parenthesis plus 2 space space space end cell row cell y equals 3 left parenthesis 1 right parenthesis plus 4 plus 2 space space space space space space space space space space end cell row cell y equals 3 minus 4 plus 2 space space space space space space space space space space space space space space space space end cell row cell y equals 1 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 space space space end cell end table space space
    Step 2 of 3:
    Find two solutions for y equals 8 x minus 10.
    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 8 left parenthesis 1 right parenthesis minus 10 end cell row cell y equals negative 2 space space space space space space space space space space space end cell end table
    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 8 left parenthesis 0 right parenthesis minus 10 end cell row cell y equals negative 10 space space space space space space space end cell end table
    Step 3 of 3:
    Plot the set of coordinate points to get the graph:

    The graphs intersect at a single point (2, 6). This is the solution of the given set of equation.
     

    The points of intersection of two sets of graphs are the corresponding solutions of the set of equations.

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