3x-y=14
9x- =-27

use the method of substitution to solve

The solution to the system of equations is x=3 y= 23  

Step-by-step explanation:

solving this system of equation using substitution method  

 -3x-y=14 …..   equation (1)    

 -9x =-27   ….. equation (2)  

Solving for value of x from equation 2  

-9x =-27    

so x= -27/-9 = 3

so x = 3

The second equation is solved for x, so we can substitute the expression 3 in for x in the first equation (1)

-3x-y=14

-3 (3) - y =14  

-9-y= 14

-9=14+y

y=-23

The solution to the system of equations is x=3 y= -23  

We can check our work by plugging these numbers back into the original equations. Let's try -3x-y=14      

-3x-y=14      

-3(3) -(-23)= 14

-9+23 = 14

14= 14

Yes, our solution checks out.

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

hello,

b) 62.47% of the students are between 14 and 18 years old.

step-by-step explanation:

mean = 15 and standard deviation = 2

student between 14 to 18

formula used z-score

for age 14 , z score

using z-table , p(z> -0.5)=0.3085

for age 18 , z score

using z-table , p(z< 1.5)=0.9332

p(-0.5< z< 1.5)=0.9332-0.3085 = 0.6247

thus, 62.47% of the students are between 14 and 18 years old.

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