How do you solve the system #4x-5y=-7# and #y=5x# using substitution?

1 Answer
Oct 1, 2016

Answer:

#x = 1/3 and y = 5/3#

Explanation:

There are two variables, therefore we need two equations.

#4x-5y=-7# and #color(red)(y=5x)#

#color(red)(y=5x)# means that #y and 5x# have exactly the same value.

#color(red)(y" and " 5x)# are therefore interchangeable.

#4x-5color(red)(y)=-7# has two variables and therefore cannot be solved with one unique solution. There are infinitely many answers.

Replace #color(red)(y)# by #color(red)(5x)#
This gives an equation with only ONE variable and it can be solved.

# " "4x-5color(red)(y)=-7#
#color(white)(xxxxxxx)darr#
#rarr4x-5color(red)((5x))=-7" "# (now the equation has only x)

#4x -25x = -7#

#-21x = -7" "larr div -21#

#x = 1/3#

Now find the value of #y#, knowing that #y = 5x#

#y = 5(1/3)#

#y = 5/3#