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:
11, 13 and 15.
Step-by-step explanation:
Let's say that the odd number is "x". If x is for example 15, then the next ODD number would be 15+2=17 and the one after that would be 15+2+2=15+4=19.
Applying that here, we get:
Odd number* the next odd number*the next odd number=2145
x*(x+2)*(x+4)=2145
x*(x^2+4x+2x+8)=2145
x^3+6x^2+8x=2145
By solving the polynomial, you get x=11.
Which makes our three numbers: 11, 13 and 15.
11*13*15=2145. The answer checks.
5/8 that's how ratio of students that will buy lunch. so in order to find number students who will buy the lunch out of 720, just multiply 720 with 5/8 ie, 720x5/8 ie 450.
450 is answer
Answer:
Step-by-step explanation:
You should use a ^ to indicate an exponent. x^2 is the same as x².
x² + 9x + 20
Replace the x with (-5).
(-5)² + 9(-5) + 20 = 25-45+20 = 0
Then do the same with x = (-3):
(-3)² + 9(-3) + 20 = 9 - 27 + 20 = 2
You can do x = (-6)
7•x=x-15
I think this would work, if I understood what you were saying correctly.
