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

ant101
Aug 21, 2018

#1**+1 **

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**

Guest Aug 21, 2018

#2**+1 **

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

ElectricPavlov
Aug 21, 2018