Anthony is solving a system of linear equation using substitution.

Question

6x−2y=10
y=3x−5

Which equation represents the first step for Anthony to solve the system?
A.6(3x−5)−2y=10

B.6x−2(3x−5)=10

C.6x−2x−5=10

D.6x−3x−5=10

Answer 1

To solve the system of equations using substitution, Anthony will take the second equation, \( y = 3x - 5 \), and substitute it into the first equation, \( 6x - 2y = 10 \).

So the first step will involve substituting \( y \) in the first equation:

Starting with: \[ 6x - 2y = 10 \] Substituting \( y \): \[ 6x - 2(3x - 5) = 10 \]

This corresponds to option B: \( 6x - 2(3x - 5) = 10 \).

Thus, the correct answer is B.