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>
Answer:
Whitney made 6 baskets
Step-by-step explanation:
Let the number of baskets made by Whitney be x.
The 15 baskets made by
Chiyann is equal to 2 times plus 3 what Whitney made
Mathematically what she made would be 2x + 3
To get x, we equate this equation to 15
2x + 3 = 15
2x = 12
x = 12/2
x = 6 baskets
If you draw out a coordinate plane you will see that they , on their Y access, are both nine witch means that they a horizontal line so all you have to do is subtract the x access witch is 3.
hope this helped
Answer:
Step-by-step explanation:
The number of bushels produced is given by:
The owner's income is given by:
Income is given by the price per unit multiplied by the number of units sold. Therefore, the price function can be represented as:
Answer:
0.38
Step-by-step explanation:
First, we convert the fraction to a decimal number by dividing the numerator by the denominator:
3 / 8 = 0.375
There are two parts to the decimal number above:
Integer Part: 0
Fractional Part: 375
Now, we will make the Fractional Part just two digits (nearest hundredth) by using our rounding rules.*
In this case, Rule II applies, so 3/8 (or 0.375) rounded to the nearest hundredth in decimal format is:
0.38
