Question

How many solutions does the system 2x + y = 1 and 4x + 2y = 2 have? 15 points giveaway!

Answer 1

infinite number of solutions

Explanation:

2x + y = 1 ( subtract 2x from both sides )

y = 1 - 2x → (1)

4x + 2y = 2 → (2)

substitute y = 1 - 2x into (2)

4x + 2(1 - 2x) = 2 ← distribute parenthesis and simplify left side

4x + 2 - 4x = 2

2 = 2 ← true statement

This indicates the system has an infinite number of solutions

Answer 2

infinitely many.

Explanation:

Given the equation 2x+y=1 and 4x+2y=2, if we divide the second equation by 2, we are left with 2x+y=1 which is the same equation as the first and this means that the line overlap, and that there are infinite places where they intercept.