Maths-
General
Easy

Question

Find the solution of the given system of equation.
y equals x squared plus 3 x plus 1
y equals negative x plus 1

hintHint:

An equation of the form a x squared minus x equals 0 can be solved by factorizing them into x left parenthesis a minus x right parenthesis and then equating them to zero. A quadratic equation is a polynomial with degree two.
We are asked to solve the given system of equation.

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


    Step 1 of 3:
    Eliminate the variable y by equating the equations. Thus, 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 x squared plus 3 x plus 1 equals negative x plus 1 space space end cell row cell x squared plus 3 x plus x plus 1 minus 1 equals 0 end cell row cell x squared plus 4 x equals 0 space space space space space space space space space space space space space space space space space space end cell end table
    Step 2 of 3: 
    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 plus 4 x equals 0 space end cell row cell x left parenthesis x plus 4 right parenthesis equals 0 end cell row cell x equals 0 space space space space space space space space space space space end cell row cell x plus 4 equals 0 space space space space space end cell row cell space x equals negative 4 space space space space space space space space space end cell end table
    Step 3 of 3:
    Substitute the values of x in any of the given equation to get the solutions of y.
    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 negative x plus 1 space end cell row cell y equals 0 plus 1 space space space space space end cell row cell y equals 1 space space space space space space space space space space space space end cell end table
    When x=-4,
    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 1 space space space space space space end cell row cell y equals negative left parenthesis negative 4 right parenthesis plus 1 end cell row cell y equals 4 plus 1 space space space space space space space space space space end cell row cell y equals 5 space space space space space space space space space space space space space space space space end cell end table
    Thus, the solutions are:left parenthesis 0 comma 1 right parenthesis straight & left parenthesis negative 4 comma 5 right parenthesis
     

    The elimination method is the process of eliminating one of the variables in the system of linear equations using addition or subtraction method.

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