I'm having some trouble with Linear Systems of Equations, I get the basic concept but it would be helpful if someone could do the following problem step by step.

I'm having some trouble with Linear Systems of Equations, I get the basic concept but it would be helpful if someone could do the following problem step by step.

I'm having some trouble with Linear Systems of Equations, I get the basic concept but it would be helpful if someone could do the following problem step by step.

The most fundamental way to do this is to differentiate the first equation again gettin u''= 4u'- v'. From the second equation, v'= -4u+ 4v so we can replace it: u''= 4u'- (-4u+ 4v)= 4u'+ 4u- 4v. We still have a "v" to eliiminate but from the first equation, v= 4u- u' so that becomes u''= 4u'+ 4u- 4(4u- u')= 8u' -12u. that is, u''- 8u+ 12u= 0. Solve that equation for the general solution, u, then use v= 4u- u' to find v.