Question

solve the system by substitution.

x - 3y = 4
2x - 6y = 8

a. no solution
b. x = 4, y = 0
c. x = 0, y = 0
d. infinite solutions

Explanation:

Step1: Express x from first equation

From \( x - 3y = 4 \), we get \( x = 3y + 4 \).

Step2: Substitute x into second equation

Substitute \( x = 3y + 4 \) into \( 2x - 6y = 8 \):
\( 2(3y + 4) - 6y = 8 \)
Expand: \( 6y + 8 - 6y = 8 \)
Simplify: \( 8 = 8 \).
This is a true statement, meaning the two equations are dependent (represent the same line), so there are infinite solutions.

Answer:

D. infinite solutions