Maths-
General
Easy

Question

Find the solution of the given system of equation.
y equals x squared plus 1
y equals negative 2 x

hintHint:

A quadratic equation of the form x squared plus left parenthesis a plus b right parenthesis x plus a b can be simplified to the form left parenthesis x plus a right parenthesis left parenthesis x plus b right parenthesis.The maximum possible number of solutions possible for a quadratic equation is two.
We are asked to solve the given set of equation.

The correct answer is: We are asked to solve the given set of equation.


    Step 1 of 3:
    The LHS of the given set of equation is equal. Hence, we can equate the RHS.
    So, we have:
    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 1 equals negative 2 x space space end cell row cell x squared plus 2 x plus 1 equals 0 end cell end table
    Step 2 of 3:
    Simplify the equation to get the solutions of the variable x:
    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 plus 1 equals 0 space space space space space space space space space space end cell row cell x squared plus x plus x plus 1 equals 0 space space space space space space space end cell row cell x left parenthesis x plus 1 right parenthesis plus 1 left parenthesis x plus 1 right parenthesis equals 0 end cell row cell left parenthesis x plus 1 right parenthesis left parenthesis x plus 1 right parenthesis equals 0 space space space space space space space space space end cell row cell x equals negative 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 end cell row cell x equals negative 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 end cell end table
    Thus, the solutions of the x –s -1 with a multiplicity of two.
    Step 3 of 3:
    Equate the values of x in any of the equations to get the value of y:
    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 negative 2 x space space space space space space end cell row cell y equals negative 2 left parenthesis negative 1 right parenthesis end cell row cell y equals 2 space space space space space space space space space space space space space end cell end table
    Thus, the required solution is: x=-(-1, 2).
     

    Multiplicity of a value is the number of times the value repeats as the solution of a particular equation.

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