Mathematics, 19.06.2020 21:57 jpsaad00

Solve the simultaneous equation
y=9-x
y= 2x^2+4x+6

Answers: 2

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Answer from: katey3809

The solution to the given simultaneous equation is (1/2, 8 1/2) and (-3, 12)

From the question,

We are to solve the given simultaneous equations

The given equations are

y = 9-x (1)

y = 2x²+4x+6 (2)

Substitute equation (1) into equation (2)

y = 2x²+4x+6

That is

9-x = 2x²+4x+6

Simplifying, we get

0 = 2x² +4x +x +6 -9

0 = 2x² +5x -3

∴ 2x² +5x -3 = 0

Now, solving the quadratic equation

2x²+6x -x -3 = 0

Factorizing

2x(x+3) -1(x+3) = 0

Then, we get

(2x -1)(x+3) = 0

∴ 2x - 1 = 0 OR x + 3 = 0

2x = 1 OR x = -3

∴ x = 1/2 OR x = -3

Now, substitute the values of x into equation (1) to determine the values of y

y = 9-x

When x = 1/2

y = 9 - 1/2

y = 8 1/2

and when x = -3

y = 9 --3

y = 9+3

y = 12

Hence, the solution to the given simultaneous equation is (1/2, 8 1/2) and (-3, 12)

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Answer from: winterchadrick

The solution of the given two simultaneous equation

A( 3 ,6) and $B(\frac{1}{2} ,\frac{17}{2} )$

The intersecting points of given two simultaneous equations are

A( 3 ,6) and $B(\frac{1}{2} ,\frac{17}{2} )$

Step-by-step explanation:

Explanation:-

Step(i):-

Given simultaneous equation

y = 9-x ...(i)

y = 2 x² +4 x+6 ..(ii)

Equating (i) and (ii) equations , we get

9 -x = 2 x² +4 x+6

⇒ 2 x² +4 x + 6- 9 +x =0

⇒ 2 x² + 5 x - 3 =0

⇒ 2 x² +6 x -x -3 =0

⇒ 2 x ( x +3) -1 ( x+3) =0

⇒ (2 x -1 ) ( x+3) =0

⇒ (2 x -1 ) = 0 and ( x +3 ) =0

2 x =1 and x = -3

x = 1/2 and x =3

Step(ii):-

x = 3 ⇒ y = 9 - 3 =6

A( 3 ,6)

$x = \frac{1}{2} , y = 9 - \frac{1}{2} = \frac{17}{2}$

$B(\frac{1}{2} ,\frac{17}{2} )$

Final -

The intersecting points of two simultaneous equations are

A( 3 ,6) and $B(\frac{1}{2} ,\frac{17}{2} )$

The solution of the given two simultaneous equation

A( 3 ,6) and $B(\frac{1}{2} ,\frac{17}{2} )$

Answer from: Quest

Subtracting is the opposite of adding

Answer from: Quest

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq and the angle ∠orq are opposite, therefore:

$m\angle opq+m\angle orq=180\°\\\\m\angle opq+ (2x + 16)\°=180\°$

then, $m\angle opq+ (2x + 16)\°=180\°$ can be used to d to calculate the measure of ∠opq

Quadrilateral opqr is inscribed in circle n, as shown below. which of the following could be used to

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Solve the simultaneous equation
y=9-x
y= 2x^2+4x+6...

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