Solve the simultaneous equation below
The sum of 2 number is 8, their product is 15. Find the number.
nice guess, but Juliet has learned nothing.
X+y=8 ----------(1)
Xy=15 ----------(2)
X+y=8
Y=8-x -----------(3)
Put y=8-x in eqn (1)
xy=15
X(8-x)=15
8x-x^2-15=0
X^2-8x+15=0
(X-5)(x-3)=0
Put x=5 in eqn(1) put x=3 in eqn (1)
X+y=8 x+y=8
5+y=8 3+y=8
Y=8-5 Y=8-3
Y=3 y=5
Hence x & y =3 & 5
the equations needed are
x+y = 8
xy = 15
x + 15/x = 8
x^2 - 8x + 15 = 0
(x-5)(x-3) = 0
or, note that for x^2+bx+c=0, the sum of the roots is -b and the product of the roots is c.
x^2-8x+15 = 0
as above
To solve the simultaneous equation, let's assign variables to the two unknown numbers. Let's call the first number x and the second number y.
Given that the sum of the two numbers is 8, we can write the equation:
x + y = 8 ...(Equation 1)
We are also given that the product of the two numbers is 15, so we can write the equation:
xy = 15 ...(Equation 2)
To solve this system of equations, we can use the method of substitution or elimination. Let's use the substitution method in this case.
Rearrange Equation 1 to solve for x:
x = 8 - y
Now substitute this value of x in Equation 2:
(8 - y)y = 15
We have a quadratic equation:
8y - y^2 = 15
Rearrange the equation to make it quadratic:
y^2 - 8y + 15 = 0
Now we can solve this quadratic equation for the value of y.
We can factorize the quadratic equation:
(y - 3)(y - 5) = 0
Setting each factor equal to zero gives us two possible values for y:
y - 3 = 0 or y - 5 = 0
Solving for y gives us:
y = 3 or y = 5
Substituting these values back into Equation 1, we can find the corresponding values of x:
For y = 3:
x = 8 - y = 8 - 3 = 5
For y = 5:
x = 8 - y = 8 - 5 = 3
So the two numbers are 5 and 3.