Question

Find the value of a if $open square brackets table row cell straight a minus straight b end cell cell space space space 2 straight a plus straight c end cell row cell 2 straight a minus straight b end cell cell space 3 straight c plus straight d end cell end table close square brackets space equals space open square brackets table row cell negative 1 end cell cell space space space 5 end cell row 0 cell space 13 end cell end table close square brackets$

Solution

open square brackets table row cell straight a minus straight b end cell cell space space 2 straight a plus straight c end cell row cell 2 straight a minus straight b end cell cell space 3 straight c plus straight d end cell end table close square brackets space equals space open square brackets table row cell negative 1 end cell cell space space space 5 end cell row 0 cell space space 13 end cell end table close square brackets

Equating the corresponding elements, we get,

rightwards double arrow straight a minus straight b space equals space minus 1 comma space space 2 straight a plus straight c space equals space 5 comma space space space 2 straight a minus straight b space equals space 0 comma space space space 3 straight c plus straight d space equals space 13

Now consider the equations,
a - b = -1 and 2a - b = 0
Subtracting first equation from second, we get: a = 1

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