{y=3x+1 y=3x+7 how many soloutions

Answer 1

If you are asking how many solutions there are to the system of equations:

y = 3x + 1 and y = 3x + 7

then there are no solutions. "y" cannot be equal to both 3x + 1 AND 3x + 7. To prove it mathematically, since y = 3x + 1 AND y = 3x + 7, then 3x + 1 must equal 3x + 7

3x + 1 = 3x + 7 subtract 3x from both sides to get:

1 = 7

But 1 is never equal to 7 no matter what you pick for x, so there are no solutions.

Answer 2

Hi Loud,

I am assuming that your question is how many points in the x,y-plane satisfy both of these equations, so correct me if this is not the case.

Note that we have two linear equations:

y = 3x + 1 is the equation of a line with slope 3 which passes through the point (0,1)

y = 3x + 7 is the equation of a line with slope 3 which passes through the point (0,7)

Lines with the same slope are parallel. This means that they either never intersect, or overlap at every point (in which case, they are the same line). However, we can see that they cross the y-axis at different points, and so they must be different lines. This means that they never intersect, and thus that there are zero solutions to this system of linear equations.