Solve the system using substitution.
6+8y=30
y=12x

A. 6, −3/4
B. 3, 3/2
C. (1, 3)
D. (6, 3)

(1/4, 3)

Step-by-step explanation:

Substitution is essentially where we write one variable in terms of another, substitute that into the other equation so that we are left with 1 variable, and then solve for that variable.

Here, the second equation already shows y written in terms of x: y = 12x. Substitute this into the first equation:

6 + 8y = 30

6 + 8 * (12x) = 30

6 + 96x = 30

96x = 24

x = 24/96 = 1/4

Plug this into any of the equations to solve for y:

y = 12x

y = 12 * (1/4) = 3

The answer is (1/4, 3). *Note that none of the answer choices matches this, which means that you may have copied the answer incorrectly.*

B

Step-by-step explanation:

6x + 8y = 30

y = ½x

6x + 8(½x) = 30

6x + 4x = 30

10x = 30

x = 3

y = 3/2

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2