Question 146507
{{{R[a]*T[a]= 160}}} Start with the first equation



{{{R[a]= 160/T[a]}}} Solve for {{{R[a]}}}



{{{T[a]+T[b]=7}}} Move onto the last equation



{{{T[b]=7-T[a]}}} Solve for {{{T[b]}}}




{{{R[b]*T[b]= 240}}} Now move onto the second equation



{{{(2*R[a])*T[b]= 240}}} Plug in {{{R[b]= 2*R[a]}}}



{{{(2*(160/T[a]))*T[b]= 240}}} Plug in {{{R[a]= 160/T[a]}}}



{{{(320/T[a])*T[b]= 240}}} Multiply and simplify



{{{(320/T[a])*(7-T[a])= 240}}} Plug in {{{T[b]=7-T[a]}}}



{{{2240/T[a]-320= 240}}} Distribute



{{{2240-320T[a]= 240T[a]}}} Multiply <b>every</b> term by the LCD {{{T[a]}}}



{{{2240= 240T[a]+320T[a]}}} Add {{{320T[a]}}} to both sides



{{{2240= 560T[a]}}} Combine like terms



{{{4= T[a]}}} Divide both sides by 560 to isolate {{{T[a]}}}. So the first answer is {{{T[a]=4}}} 




{{{T[a]+T[b]=7}}} Go back to the last equation



{{{4+T[b]=7}}} Plug in {{{T[a]=4}}} 



{{{T[b]=3}}} Solve for {{{T[b]}}}



From here it's not too difficult to find {{{R[a]}}} and {{{R[b]}}}. So I'll let you finish.