Maths-
General
Easy

Question

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

hintHint:

Maximum number of solutions possible for a two degree polynomial is two.
We are asked to solve the given set of equation.a equals 1 comma b equals 3 straight & c equals 9

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


    Step 1 of 2:
    The LHS of the given set has the same value. Equate the RHS of the set to eradicate the variable y. Thus, 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 6 x plus 9 equals 3 x space space space space space space end cell row cell x squared plus 6 x minus 3 x plus 9 equals 0 end cell row cell x squared plus 3 x plus 9 equals 0 space space space space space space space space end cell end table
    Step 2 of 2 :
    Solve the equation using the quadratic formula,
    Here, a equals 1 comma b equals 3 straight & c equals 9
    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 fraction numerator negative b plus-or-minus square root of b squared minus 4 a c end root over denominator 2 a end fraction equals fraction numerator negative 3 plus-or-minus square root of left parenthesis 3 right parenthesis squared minus 4 left parenthesis 1 right parenthesis left parenthesis 9 right parenthesis end root over denominator 2 left parenthesis 1 right parenthesis end fraction end cell row cell equals fraction numerator negative 3 plus-or-minus square root of 9 minus 36 end root over denominator 2 end fraction 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 space space space space space space space space space space end cell row cell equals fraction numerator negative 3 plus-or-minus square root of negative 27 end root over denominator 2 end fraction 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 space space space space space space space space space space space space space end cell end table
    Here, we get negative value inside the root. Thus, there are  no real  roots for the set.

    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.

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