How do you determine the solution in terms of a system of linear equations for #1/2x = 4y#, #5y - x = -3#?

1 Answer
Sep 25, 2015

Answer:

#x=8#
#y=1#

Explanation:

I think the easiest method for solving this system is through substitution.

So we are given two equations:
#1/2x=4y#
#5y−x=−3#

Let's get the value of #x# in the first equation:
#1/2x=4y#
#(2)(1/2x)=(2)(4y)#
#color(blue)(x=8y)#

Now let's substitute this into the second equation:
#5y−color(blue)(x)=−3#
#5y−color(blue)((8y))=−3#
#-3y=−3#
#(-1/3)(-3y)=(-1/3)(−3)#
#(-1/3)(-3y)=(-1/3)(−3)#
#color(red)(y=1)#

Now that we know the #y# value, we can solve for the #x# value:
#color(blue)(x=8)color(red)y#
#color(blue)(x=8)color(red)((1))#
#color(blue)(x=8)#

So the solution of the system is:
#color(blue)(x=8)#
#color(red)(y=1)#