# y = 2x + 3, 2y = 4x + 6 the system of equations has _____ solution(s).

**Solution:**

There are 3 possible solutions to a system of linear equations.

- One solution - two distinct lines that do not share y-intercept or slope intercept at a point
- No solution - two distinct lines that share the same slope but not the same y-intercept never intersect and are parallel.
- Infinite solution - one distinct function represents two ways which in simplest form share the same slope and y-intercept.

Given, the equations are

y = 2x + 3

2y = 4x + 6

On simplification,

2y = 4x + 6 becomes y = 2x + 3

This implies both the equations are the same.

In other words, both equations share the same slope and y-intercept.

Therefore, the equations have infinite solutions.

## y = 2x + 3, 2y = 4x + 6 the system of equations has _____ solution(s).

**Summary:**

y = 2x + 3, 2y = 4x + 6 the system of equations has infinite solution(s).