Question

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

Answer 1

`(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`