Maths-
General
Easy

Question

Use elimination to solve the system of equations.
y equals negative x plus 4
y equals x squared minus 2

hintHint:

The elimination method is the process of eliminating one of the variables in the system of linear equations using addition or subtraction methods.
We are asked to solve the set of equations by the method of elimination.

The correct answer is: We are asked to solve the set of equations by the method of elimination.


    Step 1 of 3:

    The set of equations are:

                                            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 negative x plus 4 end cell row cell y equals x squared minus 2 space space space end cell end table


    Eliminating the variable y, from the equations by equating them, we get:

                                    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 negative 2 plus x squared equals 4 minus x space space space space space space end cell row cell negative 2 plus x squared minus 4 plus x equals 0 end cell row cell x squared plus x minus 6 equals 0 space space space space space space space space end cell row cell x squared plus x minus 6 equals 0 space space space space space space space space end cell end table


    Step 2 of 3:

    Using the method of factorization we, get:

                                        x squared plus x minus 6 equals 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 x squared plus 2 x minus 3 x minus 6 equals 0 space space space end cell row cell x left parenthesis x plus 2 right parenthesis minus 3 left parenthesis x plus 2 right parenthesis equals 0 end cell row cell left parenthesis x minus 3 right parenthesis left parenthesis x plus 2 right parenthesis equals 0 space space space space space space space space space end cell row cell x equals 3 straight & x equals negative 2 space space space space space space space space space space space space end cell end table space

    Thus, the solutions are:

                                                    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 x equals 3 space space space end cell row cell x equals negative 2 end cell end table

    Step 3 of 3:

    Substitute the values of x in any of the equation to get the value of y.

    When x=3,

                                             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 negative x plus 4 end cell row cell y equals negative 3 plus 4 end cell row cell y equals 1 space space space space space space space space space space end cell end table

    When x=-2,

                                         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 negative x plus 4 space space space space space space end cell row cell y equals negative left parenthesis negative 2 right parenthesis plus 4 end cell row cell y equals 2 plus 4 space space space space space space space space space space end cell row cell y equals 6 space space space space space space space space space space space space space space space space space end cell end table



    Note:
    For any equation of the form:x squared plus left parenthesis a plus b right parenthesis x plus a b, the solutions are:x equals negative a straight & x equals negative b.






     

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