Question

how many solutions does the system of equations have?
y-5x=-6
3y-15x=-12

Answer 1

To find the number of solutions for this system of equations, we need to determine if the lines represented by the equations are parallel, coincident (overlapping), or intersecting at a single point.

We can start by rewriting the second equation to simplify:

3y - 15x = -12
Divide both sides by 3 to get:
y - 5x = -4

Comparing the two equations, we can see that they have the same slope. Both equations can be rewritten in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept:

y - 5x = -6
y = 5x - 6

y - 5x = -4
y = 5x - 4

Since both equations have the same slope of 5, the lines represented by the equations are parallel. Parallel lines never intersect, so there is no solution for this system of equations.