Looking at the first system of equations,
16x - 10y = 10
-8x - 6y = 6
If we multiply both sides of the second equation by 2, the coefficient of x is exactly the negative of the coefficient of x in the first equation.
-8x - 6y = 6
⇒ 2 (-8x - 6y) = 2 (6)
⇒ -16x - 12y = 12
By combining this new equation with the first one, we can eliminate x and solve for y :
(16x - 10y) + (-16x - 12y) = 10 + 12
⇒ -22y = 22
⇒ y = -1
Then we just solve for x by replacing y in either equation.
16x - 10y = 10
⇒ 16x - 10 (-1) = 10
⇒ 16x + 10 = 10
⇒ 16x = 0
⇒ x = 0
The main idea behind elimination is combining the given equations in just the right amount so that one of the variables disappears. The "right amount" involves using the LCM of the coefficients of a given variable. In this example, the x-coefficients had LCM(8, 16) = 16, so we only had to scale one of the equations (the one with -8x) to cancel all the x terms.
If we wanted to eliminate y first instead, we first note that LCM(6, 10) = 30. To get 30 as a coefficient on y, in the first equation we would have multiplied by 3:
16x - 10y = 10
⇒ 3 (16x - 10y) = 3 (10)
⇒ 48x - 30y = 30
And in the second equation, we would have multiplied by -5 (negative so that upon combining the equations, we end up with -30y + 30y = 0):
-8x - 6y = 6
⇒ -5 (-8x - 6y) = -5 (6)
⇒ 40x + 30y = -30
Now combining the two scaled equations gives
(48x - 30y) + (40x + 30y) = 30 + (-30)
⇒ 88x = 0
⇒ x = 0
We then solve for y :
16x - 10y = 10
⇒ -10y = 10
⇒ y = -1
so we end up with the same solution as before.
The reciprocal of a number is the number that the first number will multiply with that equals one.
So, for instance, the reciprocal of 3 is 1/3.
Since we can write 3 as 3/1, we can see it's simply flipping the numerator and denominator to find the reciprocal.
So, flipping numerator and denominator, the reciprocal of 31/2 is 2/31.
Question:
Chucky grabbed 11 items in the grocery store that each had a different price and had a mean cost of about $4.44. On his way to the register, he gave in to an impulse to add a 12th item: an entire wheel of cheese that cost $39.99.
How will adding the wheel of cheese affect the mean and median?
Answer:
There will be a big difference in the mean when the new item is added
Step-by-step explanation:
Given
Before we solve further, we need to first calculate the total amount of the 11 items.
Make Total the Subject of formula
When the 12th item of $39.99 is added, the new mean becomes.
By comparing this the old mean, we can see a huge increment between $4.44 and $7.4025
This means that there will be a big difference in the mean when the new item is added.
For the Median:
The old mean shows that the prices of the 11 items is within a small range from $4.44.
So, when the new item is added the median will only change a little bit.
In other words, the median value will only change a little bit.
Answer:
x = 1
Step-by-step explanation:
4x-5=y
4x-5= -1
4x = -1+5
4x=4
x=1
2x-y=3
2x-(-1)=3
2x+1=3
2x= 3-1
2x= 2
x=1
since the two answers for x are the same therefore:
x = 1
Answer:
Its B
Step-by-step explanation:
