How do you solve the system of equations #-8x - 5y = 24# and #5x - 7y = - 15#?

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Answer 1 · 2018-06-30T00:51:48

#(-3,0)#

Let's start with the second equation

#5x-7y=-15#

When it comes to systems of equations, we can solve for one variable in terms of the other. Let's solve for #x# by adding #7y# to both sides.

#5x=7y-15#

#color(blue)(x=7/5y-3)#

Now, let's plug this value of #x# into our first equation:

#-8color(blue)((7/5y-3))-5y=24#

Simplifying by distributing, we get

#-56/5y+24-5y=24#

#=-56/5y-5y=0#

Let's get common denominators:

#-56/5y-25/5y=0#

#-81/5y=0#

#color(red)(y=0)#

Now, let's plug this in for our equation for #x# in blue:

#x=7/5 (0)-3#

#color(blue)(x=-3)#

Therefore, our solution is at the point

#(-3,0)#

Hope this helps!