How do you solve the system of equations #5s + 3t = 24# and #7s - 6t = 20#?

1 Answer
May 1, 2018

# t = 4/3 #

# s = 4#

Explanation:

This type of question is known as simultaneous equations. It can be solved using substitution, which is one of the methods of solving it.

#5s + 3t = 24# ⇒ EQN #1#

#7s - 6t = 20# ⇒ EQN #2#

#(24-3t)/5 = s# ⇒ EQN #3#

Substitute EQN #3# into EQN #2#

#7* (24-3t)/5 - 6t = 20#

#(168-21t)/5 -6t =20#

⇒ Multiply the whole EQN by 5 to solve it easier.

#168-21t - 30t = 100#

#-51t = -68#

#t = 4/3#

When #t = 4/3# ,

#5s + 3*(4/3) = 24#

#5s = 20#

#s = 4#

Check if it's correct by inserting the values found.

#5(4) + 3*(4/3) = 24#

#7(4) - 6(4/3) = 20#