Answer:
Solving systems of equations with 3 variables is very similar to how we solve systems with two variables. When we had two variables we reduced the system down
to one with only one variable (by substitution or addition). With three variables
we will reduce the system down to one with two variables (usually by addition),
which we can then solve by either addition or substitution.
To reduce from three variables down to two it is very important to keep the work
organized. We will use addition with two equations to eliminate one variable.
This new equation we will call (A). Then we will use a different pair of equations
and use addition to eliminate the same variable. This second new equation we
will call (B). Once we have done this we will have two equations (A) and (B)
with the same two variables that we can solve using either method. This is shown
in the following examples.
Example 1.
3x +2y − z = − 1
− 2x − 2y +3z = 5 We will eliminate y using two different pairs of equations
5x +2y − z = 3
Step-by-step explanation:
Answer:
Distance = 45 meters
Time = 3 seconds
Step-by-step explanation:
Here, we want to calculate distance and time
To find the time, we can use one of the Newtons law of motion
V = U + at
In this question
V = final velocity = 18 m/s
U = initial velocity = 12 m/s
a = acceleration
Thus;
18 = 12 + 2(t)
18-12 = 2t
2t = 6
t = 6/2
t = 3 seconds
Mathematically we can also find the distance using one of the equation of motion;
D = ut + 1/2 at^2
D = 12(3) + 1/2 * (2) * 3^2
D = 36 + 9
D = 45 m
Answer: Use distributive property
Step-by-step explanation:
Answer:she spent 10 hours working in her aunt's store last week.
Step-by-step explanation:
Let x represent the number of hours that Lee spent working at the movie theater.
Let y represent the number of hours that Lee spent working at her aunt's store.
Lee worked a total of 30 hours at the movie theater and her aunt's store. This means that
x + y = 30
Her combined pay from the jobs was $240. She earned $9 per hour working at the movie theater and $6 per hour working in her aunt's store. This means that
9x + 6y = 240 - - - - - - - - - -1
Substituting x = 30 - y into equation 1, it becomes
9(30 - y) + 6y = 240
270 - 9y + 6y = 240
- 9y + 6y = 240 - 270
- 3y = - 30
y = - 30/ - 3 = 10 hours
This question is worded badly, so don't be alarmed.
Obviously if this were a square patter the number of red tiles could only be 1,4,9,16,25,36 etc and this is not the numbers given...It would help tremendously if they gave you another reference point so as to know how the tiles were being laid out.
If they are laid out alongside one another with a consistent border for each you wouldn't need 12 blue tiles for each red tile either...if two were laid side by side you would only need 20 blue tiles to have the border around both...you see how the arrangement makes a huge difference and you are given no details as to what that arrangement is...
So just to keep it simple, assume that each red tile is surrounded by 12 blue tiles....
Total tiles equals r+12r=13r
t=13r so
t(15)=195, t(20)=260, t(25)=325, t(30)=390
