What is the solution to this system of equations? 2t + w = 10 4t = 20 − 2w A. It has no solution. B. It has infinite solutions. C. It has a single solution: t = 4, w = 2. D. It has a single solution: t = 2, w = 6. E. It has a single solution: t = 6, w = -2.

Step-by-step explanation:

Given the system of equations:

2t + w = 10 1

4t = 20 − 2w ... 2

From 1:

w = 10-2t ...3

Substitute 3 into 2 to have;

4t = 20 - 2(10-2t)

4t = 20-20+4t

4t = 4t

Let t = k

Substitute t = k into 1 and get w;

From 1: 2t + w = 10

2k + w =10

w = 10 - 2k

k can take any integers. This shows that the solution to the equation is infinite

1.4

2.3

step-by-step explanation:

the formula for the constant of variation is

y= kx

divide each side by x

y/x =kx/x

y/x =k

we know a and y

1.   y/x = k

4/1 =4

check the other values to make sure they are the same

8/2 = 4   12/3 =4   and 16/4 =4  

the constant of variation is 4

2.   y/x = k

3/1 =3

check the other values to make sure they are the same

6/2 = 3   9/3 =3   and 12/4 =3  

the constant of variation is 3