+885 Here is a cool question! Find an ordered pair \((u,v)\) that solves the system: \(\begin{align*} 5u &= -7 - 2v,\\ 3u &= 4v - 25 \end{align*}\) .
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
+37146 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
