Question

Which of these shows the result of using the first equation to substitute for Y in the second equation, then combining like terms?

y= 2x
2x + 3y = 16
A. 5y= 16
B. 5x= 16
C. 4x= 16
D. 8x= 16

Answer 1

To solve the system of equations, substitute y = 2x into the second equation 2x + 3y = 16, combine like terms to get 8x = 16, and then divide both sides by 8 to find x = 2. The correct choice is D. 8x = 16.

Step-by-step explanation:

The student has asked how to substitute the first equation for y in the second equation and then combine like terms. The original equations are:

y = 2x

2x + 3y = 16

First, we substitute the expression for y from the first equation into the second equation:

2x + 3(2x) = 16

This simplifies to:

2x + 6x = 16

Combining like terms (the terms with x), we get:

8x = 16

This can be further simplified by dividing both sides of the equation by 8, giving us:

x = 2

The option that shows the result of the substitution and the combination of like terms is:

D. 8x = 16