Maths-
General
Easy

Question

Find the solution of the system of equations.
y equals 7 x squared plus 12
y equals 14 x plus 5

hintHint:

The expansion of the identity  left parenthesis x minus a right parenthesis squared text  is  end text x squared minus 2 a x plus a squared . A polynomial of degree has at most two real solutions.
We are asked to solve the set of equation.

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


    Step 1 of 3
    The LHS of the given set of equation is the same. Hence, equate them to eliminate a variable. Thus, we get:
    table attributes columnalign right columnspacing 0em end attributes row cell 7 straight x squared plus 12 equals 14 straight x plus 5 space space space space space end cell row cell 7 straight x squared minus 14 straight x plus 12 minus 5 equals 0 end cell row cell 7 straight x squared minus 14 straight x plus 7 equals 0 space space space space space space space space space end cell row cell straight x squared minus 2 straight x plus 1 equals 0 space space space space space space space space space space space space space space end cell end table
    We factorized seven out of the equation to simplify it.
    step 2 of 3
    Now, solve the simplified equation:
    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 minus 2 x plus 1 equals 0 space space space space space space space space space space space space space end cell row cell x squared minus x minus x plus 1 equals 0 space space space space space space space space end cell row cell x left parenthesis x minus 1 right parenthesis minus 1 left parenthesis x minus 1 right parenthesis equals 0 end cell row cell left parenthesis x minus 1 right parenthesis left parenthesis x minus 1 right parenthesis equals 0 space space space space space space space space space end cell row cell left parenthesis x minus 1 right parenthesis squared equals 0 space space space space space space space space space space space space space space space space space space end cell row cell therefore x 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 end cell end table
    Here, the multiplicity of the solution is two.
    Step 3 of 3
    Substitute the found value of  in any of the equation, to find 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 14 x plus 5 end cell row cell y equals 14 left parenthesis 1 right parenthesis plus 5 end cell row cell y equals 14 plus 5 end cell row cell y equals 19 end cell end table
    Thus, the solution is (1,19).

    The multiplicity of a solution is the number of times that value appears to be a solution of an equation.

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