Question

Y = 2x + 3 2y = 4x + 6 The system of equations has _____ solution(s).

A. no
B. one
C. infinite

Answer 1

C. infinite

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.