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# Cool Question!

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Here is a cool question! Find an ordered pair $$(u,v)$$ that solves the system: \begin{align*} 5u &= -7 - 2v,\\ 3u &= 4v - 25 \end{align*} .

Aug 21, 2018

#1
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Solve the following system:
{5 u = -2 v - 7 | (equation 1)
3 u = 4 v - 25 | (equation 2)

Express the system in standard form:
{5 u + 2 v = -7 | (equation 1)
3 u - 4 v = -25 | (equation 2)

Subtract 3/5 × (equation 1) from equation 2:
{5 u + 2 v = -7 | (equation 1)
0 u - (26 v)/5 = (-104)/5 | (equation 2)

Multiply equation 2 by -5/26:
{5 u + 2 v = -7 | (equation 1)
0 u+v = 4 | (equation 2)

Subtract 2 × (equation 2) from equation 1:
{5 u+0 v = -15 | (equation 1)
0 u+v = 4 | (equation 2)

Divide equation 1 by 5:
{u+0 v = -3 | (equation 1)
0 u+v = 4 | (equation 2)

u = -3
v = 4

Aug 21, 2018
#2
+15451
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Multiply first equation by 2 :   10u = -14-4v

add to second equation :   13u = -39       so u= - 3

Sustitute this result in to one of the equations:   5(-3) = -7-2v    Solve:  v= 4

Aug 21, 2018