Answer:
(4, 2 ) and (2, 4 )
Step-by-step explanation:
xy = 8 → (1)
y = - x + 6 → (2)
substitute y = - x + 6 into (1)
x(- x + 6) = 8
- x² + 6x = 8 ( subtract 8 from both sides )
- x² + 6x - 8 = 0 ( multiply through by - 1 )
x² - 6x + 8 = 0 ← in standard form
(x - 4)(x - 2) = 0 ← in factored form
equate each factor to zero and solve for x
x - 4 = 0 ⇒ x = 4
x - 2 = 0 ⇒ x = 2
substitute these values into (2) for corresponding values of y
x = 4 : y = - 4 + 6 = 2 ⇒ (4, 2 )
x = 2 : y = - 2 + 6 = 4 ⇒ (2, 4 )
Answer: 67.5 cm
Step-by-step explanation:
Jason has 4 lengths of ropes
first is 
second is 
Third is ![0.3\ m\approx 30\ cm\quad [\text{1 m = 100 cm}]](https://tex.z-dn.net/?f=0.3%5C%20m%5Capprox%2030%5C%20cm%5Cquad%20%5B%5Ctext%7B1%20m%20%3D%20100%20cm%7D%5D)
fourth is ![0.5\ ft\approx 6\ in.\approx 15\ cm\quad [\text{1 ft=12 in.}]](https://tex.z-dn.net/?f=0.5%5C%20ft%5Capprox%206%5C%20in.%5Capprox%2015%5C%20cm%5Cquad%20%5B%5Ctext%7B1%20ft%3D12%20in.%7D%5D)
the total length of rope is the sum of four lengths
Answer:
- The system of equations is x + y = 85 and 7/20x+2/5y=31
- To eliminate the x-variable from the equations, you can multiply the equation with the fractions by 20 and multiply the other equation by -7.
- B-She used 60 minutes for calling and 25 minutes for data.
Step-by-step explanation:
It is always a good idea to start by defining variables in such a problem. Here, we can let x represent the number of calling minutes, and y represent the number of data minutes. The the total number of minutes used is ...
x + y = 85
The total of charges is the sum of the products of charge per minute and minutes used:
7/20x + 2/5y = 31.00
We can eliminate the x-variable in these equations by multiplying the first by -7 and the second by 20, then adding the result.
-7(x +y) +20(7/20x +2/5y) = -7(85) +20(31)
-7x -7y +7x +8y = -595 +620 . . . . eliminate parentheses
y = 25 . . . . . . . . simplify
Then the value of x is
x = 85 -y = 85 -25
x = 60
Let the sister be x years old.
Then Jessica is x + 5 years old.
Their ages add to 47.
x + x + 5 = 47
2x + 5 = 47
2x = 42
x = 21
x + 5 = 26
Jessica is 26, and her sister is 21.
First group the coefficients together on their side of the equal sign.
-x + 3x = 2x.
Then, since it is a positive number, subtract it from that side and the other side.
On the other side, the x becomes -x.
Add the 6 from the other side to the 8 to make 14.
14 = -x
Divide both sides by -1, to get the answer.
x = -14
