Question

how many solutions does this system of equations have?
$2x + y = 1$
$4x + 2y = 2$

Explanation:

Step1: Simplify the second equation

Divide $4x+2y=2$ by 2:
$\frac{4x}{2}+\frac{2y}{2}=\frac{2}{2}$
$2x+y=1$

Step2: Compare the two equations

The simplified second equation is identical to the first equation $2x+y=1$. This means the two lines are the same, overlapping completely.

Step3: Determine number of solutions

Overlapping lines have infinitely many points in common, so there are infinitely many solutions.

Answer:

Infinitely many solutions