Respuesta :
Answer:
The solution of the given two simultaneous equation
A( 3 ,6) and [tex]B(\frac{1}{2} ,\frac{17}{2} )[/tex]
The intersecting points of given two simultaneous equations are
A( 3 ,6) and [tex]B(\frac{1}{2} ,\frac{17}{2} )[/tex]
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
[tex]2 x =1[/tex] and x = -3
x = 1/2 and x =3
Step(ii):-
x = 3 ⇒ y = 9 - 3 =6
A( 3 ,6)
[tex]x = \frac{1}{2} , y = 9 - \frac{1}{2} = \frac{17}{2}[/tex]
[tex]B(\frac{1}{2} ,\frac{17}{2} )[/tex]
Final answer:-
The intersecting points of two simultaneous equations are
A( 3 ,6) and [tex]B(\frac{1}{2} ,\frac{17}{2} )[/tex]
The solution of the given two simultaneous equation
A( 3 ,6) and [tex]B(\frac{1}{2} ,\frac{17}{2} )[/tex]
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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