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.


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