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

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Answer 1 · 2018-05-01T10:53:19

# t = 4/3 #

# s = 4#

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# √