Maths-
General
Easy

Question

Find the solution of the system of equations.
y equals 0.75 x squared plus 4 x minus 5
y = 4x - 5

hintHint:

Hint:
A polynomial of degree two have at most two real solutions. Factorization is the process of factorizing an equation or an expression.
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 has the same value. So, we could equate the RHS of the set. 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 0.75 x squared plus 4 x minus 5 equals 4 x minus 5 space space space space space space end cell row cell 0.75 x squared plus 4 x minus 4 x minus 5 plus 5 equals 0 end cell row cell 0.75 x squared 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 row cell 75 x squared 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 space space space end cell end table
    Here, we multiply the equation by ten to remove the decimal.
    Step 2 of 3:
    Solve the equation to find the variable of 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 75 x squared equals 0 space space space space space space end cell row cell x squared equals 0 space space space space space space space space space space end cell row cell x equals 0 straight & x equals 0 end cell end table
    Here, the solution is  x = 0 with a multiplicity of two.
    Step 3 of 3:
    Substitute the value of x in any of the equation to get the value 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 4 x minus 5 end cell row cell y equals 0 minus 5 space space space end cell row cell y equals negative 5 space space space space space space end cell end table
    Thus, the required solution is (0, -5).

    The multiplicity of a value is the number of times it repeats itself.

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