Maths-
General
Easy

Question

Find the solution of the system of equations.
y equals 6 x squared plus 3 x minus 11
y = 3x - 5

hintHint:

Hint:
An expression of the form  (x2 - a2) can be simplified into (x - a) (x + a). The solutions can be found by equating them to zero.
We are asked to solve the set of equation.
Substitute the values of  in any of the equation to get the values of y.

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


    Step 1 of 3 :
    The LHS of the given set has the same value. So, equate the RHS of the set. 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 6 x squared plus 3 x minus 11 equals 3 x minus 5 space space space space space space space space space end cell row cell 6 x squared plus 3 x minus 3 x minus 11 plus 5 equals 0 space space space end cell row cell 6 x squared minus 6 equals 0 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 6 open parentheses x squared minus 1 close parentheses equals 0 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 x squared minus 1 equals 0 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
    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 minus 1 equals 0 space space space space space space space space space space space space space space space space space space space space end cell row cell left parenthesis x plus 1 right parenthesis left parenthesis x minus 1 right parenthesis equals 0 space space space space space space space space space space end cell row cell left parenthesis x plus 1 right parenthesis equals 0 straight & left parenthesis x minus 1 right parenthesis equals 0 end cell row cell x equals negative 1 straight & x equals 1 space space space space space space space space space space space space space end cell end table
    Step 3 of 3:
    Substitute the values of  in any of the equation to get the values 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 3 x minus 5 space space space space space space end cell row cell y equals 3 left parenthesis negative 1 right parenthesis minus 5 end cell row cell y equals negative 3 minus 5 space space space space space end cell row cell y equals negative 8 space space space space space space space space space space space space end cell end table space
    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 3 x minus 5 space space end cell row cell y equals 3 left parenthesis 1 right parenthesis minus 5 end cell row cell y equals 3 minus 5 space space space space space end cell row cell y equals negative 2 space space space space space space space end cell end table
    Thus, the required solutions are ( -1,-8) and (1,-2)


    You could solve a set of equations by graphing them. The points where the graphs intersect are the solutions.

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