Hi Mike… can you solve this and explain please? Thanks!
ax + 5y = 8
12x + 15y = 10
In the given system of equations, a is a constant. If the system has no solutions, what is the value of a ?
When a linear system has no solutions, that means the lines formed by the equations are parallel—they never intersect, so there is never a points that satisfies both equations. And of course, parallel lines have equal slopes.
So, let’s put both of these equations into slope-intercept form:
All we care about are the slopes, so let’s set those equal and solve.