Determine the number of solutions to this system of linear equations: y=7x−3 y=7x+3

Answer 1

To determine the number of solutions to the system of equations given by:

1. $y=7x-3$
2. $y=7x+3$

we start by observing the structure of the equations. Both equations are in the slope-intercept form $y=mx+b$, where $m$ is the slope and $b$ is the y-intercept.

• The slope of the first equation $y=7x-3$ is $7$, and its y-intercept is $-3$.
• The slope of the second equation $y=7x+3$ is also $7$, but its y-intercept is $3$.

Since the slopes of both lines are equal (both are $7$), the lines are parallel. Parallel lines do not intersect, which means they have no points in common.

Therefore, the number of solutions to the system of equations is:

$$\boxed{{\displaystyle 0}}$$