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Maths-

General

Easy

Question

Find the solution of the system of equations.
$y equals negative 2 x squared plus 6 x minus 7$
y = 13 - 2x

hint Hint:

Hint:
The quadratic formula corresponding to the equation ax² +bx + c = 0 is $fraction numerator negative b plus-or-minus square root of b squared minus 4 a c end root over denominator 2 a end fraction$ .
We are asked to solve the given set of equation..

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

Step 1 of 2:
The LHS of the set of equation has the same value. Thus, equate the RHS of the equations.
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 13 minus 2 x equals negative 2 x squared plus 6 x minus 7 space space end cell row cell 2 x squared minus 6 x minus 2 x plus 13 plus 7 equals 0 end cell row cell 2 x squared minus 8 x plus 20 equals 0 space space space space space space space space space space space space space space end cell row cell x squared minus 4 x plus 10 equals 0 space space space space space space space space space space space space space space space space space end cell end table$
We factorize the two out of the equation to get the simplified form.
Step 2 of 2:
Solve the simplified equation using the quadratic formula.
here; $a equals 1 comma b equals negative 4 straight & c equals 10$
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell fraction numerator negative b plus-or-minus square root of b squared minus 4 a c end root over denominator 2 a end fraction equals fraction numerator negative left parenthesis negative 4 right parenthesis plus-or-minus square root of left parenthesis negative 4 right parenthesis squared minus 4 left parenthesis 1 right parenthesis left parenthesis 10 right parenthesis end root over denominator 2 left parenthesis 1 right parenthesis end fraction end cell row cell equals fraction numerator 4 plus-or-minus square root of 16 minus 40 end root space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space over denominator 2 end fraction end cell row cell equals fraction numerator 4 plus-or-minus square root of negative 36 end root over denominator 2 end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space end cell end table$
Here, a negative value comes in the root. So, there exists no real root corresponding to the equation.

It is not necessary that every single quadratic equation would have two sets of real solution.

Related Questions to study

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Which sentence has the same meaning?
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b) From your scatter plot, describe the general relationship between the number of photos and the number of words per page. Use the words positive, negative, strong correlation or weak correlation.

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a) Sketch a scatter plot using ‘Number of photos’ on the horizontal axis and ‘Number of words’ on the vertical axis.
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parallel

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Find the solution of the system of equations.
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y = 4x - 5

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a) Draw a scatter plot for the data.
b) Describe the correlation between x and y as positive or negative.
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A )Draw a scatter plot for the data with ‘Diameter’ on the vertical axis and ‘Fertilizer’ on the horizontal axis. Label the points A, B, C, D and E.
b)Which garden bed appears to go against the trend?
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b)Which garden bed appears to go against the trend?
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parallel

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b) Is there positive, negative or no correlation between x and y?
c) Fit a line of best fit by eye to the data on the scatter plot.
d) Use your line of best fit to estimate:
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parallel

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By completing scatter plots for each of the following data sets, describe the correlation between x and y as positive, negative or none.

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