The system is:
i) <span>2x – 3y – 2z = 4
ii) </span><span>x + 3y + 2z = –7
</span>iii) <span>–4x – 4y – 2z = 10
the last equation can be simplified, by dividing by -2,
thus we have:
</span>i) 2x – 3y – 2z = 4
ii) x + 3y + 2z = –7
iii) 2x +2y +z = -5
The procedure to solve the system is as follows:
first use any pairs of 2 equations (for example i and ii, i and iii) and equalize them by using one of the variables:
i) 2x – 3y – 2z = 4
iii) 2x +2y +z = -5
2x can be written as 3y+2z+4 from the first equation, and -2y-z-5 from the third equation.
Equalize:
3y+2z+4=-2y-z-5, group common terms:
5y+3z=-9
similarly, using i and ii, eliminate x:
i) 2x – 3y – 2z = 4
ii) x + 3y + 2z = –7
multiply the second equation by 2:
i) 2x – 3y – 2z = 4
ii) 2x + 6y + 4z = –14
thus 2x=3y+2z+4 from i and 2x=-6y-4z-14 from ii:
3y+2z+4=-6y-4z-14
9y+6z=-18
So we get 2 equations with variables y and z:
a) 5y+3z=-9
b) 9y+6z=-18
now the aim of the method is clear: We eliminate one of the variables, creating a system of 2 linear equations with 2 variables, which we can solve by any of the standard methods.
Let's use elimination method, multiply the equation a by -2:
a) -10y-6z=18
b) 9y+6z=-18
------------------------ add the equations:
-10y+9y-6z+6z=18-18
-y=0
y=0,
thus :
9y+6z=-18
0+6z=-18
z=-3
Finally to find x, use any of the equations i, ii or iii:
<span>2x – 3y – 2z = 4
</span>
<span>2x – 3*0 – 2(-3) = 4
2x+6=4
2x=-2
x=-1
Solution: (x, y, z) = (-1, 0, -3 )
Remark: it is always a good attitude to check the answer, because often calculations mistakes can be made:
check by substituting x=-1, y=0, z=-3 in each of the 3 equations and see that for these numbers the equalities hold.</span>
A: To find the rate in feet per minute, we can use the information given.
Every two minutes, the submarine dives 300 feet. So
.
In order to confirm that our rate is correct, we can use the second set of information given.
=
.
Since we know that the rate is 150 feet per minute, we can multiply it by any number of minutes and get the answer of how deep the submarine is. We can use a variable x to represent the number of minutes and y to represent the depth in feet.
There's our equation.
B: It would be more reasonable to use an equation with the rate feet per minute because it is more accurate since the time interval isn't too big.
She will pay 90 because the income is 5 times greater
(answer o number one)
The outcomes with neither die showing 2 is 25
<h3>How to determine the outcomes with neither die showing 2?</h3>
The sample sizes of the dice are given as:
Blue die = 6
Red die = 6
The outcomes with neither die showing 2 is
Outcomes = Red die * blue die - (blue die + red die) + 1
So, we have:
Outcomes = 6 * 6 - (6 + 6) + 1
Evaluate
Outcomes = 25
Hence, the outcomes with neither die showing 2 is 25
Read more about dice at:
brainly.com/question/13632618
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Answer:
36 minutes
Step-by-step explanation:you look at it and solve it
