We have: #5 x + 8 y = - 2 and 4 x + 7 y = 6 x#
Let's solve both equations for #y#:
#Rightarrow 8 y = - 5 x - 2 and 7 y = 6 x - 4 x#
#Rightarrow y = frac(- 5 x - 2)(8) and y = frac(2 x)(7)#
Then, let's set the two expressions for #y# equal to each other:
#Rightarrow frac(- 5 x - 2)(8) = frac(2 x)(7)#
#Rightarrow 7 times (- 5 x - 2) = 8 times 2 x#
#Rightarrow - 35 x - 14 = 4 x#
#Rightarrow - 35 x - 4 x - 14 = 0#
#Rightarrow - 39 x - 14 = 0#
#Rightarrow - 39 x = 14#
#therefore x = - frac(14)(39)#
Now that we have a value of #x#, let's find #y# using one of the expressions:
#Rightarrow y = frac(2 x)(7)#
#Rightarrow y = frac(2 times - frac(14)(39))(7)#
#Rightarrow y = frac(- frac(28)(39))(7)#
#Rightarrow y = frac(- frac(28)(39))(frac(7)(1))#
#Rightarrow y = - frac(28)(39) times frac(1)(7)#
#Rightarrow y = - frac(28 times 1)(39 times 7)#
#Rightarrow y = - frac(28)(273)#
#therefore y = - frac(4)(39)#
Therefore, the solutions to the equation are #x = - frac(14)(39)# and #y = - frac(4)(39)#.
