How do you solve the following system using substitution?: 3s-5t=-30, 7s+11t=32

1 Answer
Alan P.
Oct 23, 2015

(s,t)=(-5/2,9/2) = (-2 1/2, 4 1/2)

Explanation:

Given
[1]color(white)("XXX")3s-5t=-30
[2]color(white)("XXX")7s+11t=32

Rewriting [1] to generate an equation of the form: s = some expression
[3]color(white)("XXX")3s = 5t-30

[4]color(white)("XXX")s = (5t-30)/3

We can now substitute (as per the question) ((5t-30)/3) for s in [2]
[5]color(white)("XXX")7((5t-30)/3)+11t = 32

Simplifying
[6]color(white)("XXX")(35t-210 +33t)/3 = 32

[7]color(white)("XXX")(68t-210) = 96

[8]color(white)("XXX")68t = 306

[9]color(white)("XXX")t = 9/2

Substituting 9/2 into [1] in place of t
[10]color(white)("XXX")3s -5*(9/2) = -30

[11]color(white)("XXX")3s = (5*9 -2*30)/2

[12]color(white)("XXX")3s =-15/2

[13]color(white)("XXX")s = - 5/2

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