Question

y = 2x + 3 2y = 4x + 6 The system of equations has _____ solution(s).
A. no
B. one
C. infinite

Answer 1

Answer:

C. infinite

Step-by-step explanation:

We want to solve the system:

First equation: $y=2x+3$

Second equation: $2y=4x+6$

Multiply the first equation by 2.

This gives us:

Third equation: $2y=4x+6$

Subtract the third equation to obtain;

$2y-2y=4x-4x+6-6$

$0=0$

This implies that, the solution is all real numbers.

This means that the two lines coincide with each other. Therefore there are infinitely many solutions.