How do solve the following linear system?: # 4x+21y=6 , 4x-3y=1 #?

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Answer 1 · 2016-03-23T16:37:29

The solution for the system of equations is:
#color(green)(x =13/32 #

#color(green)(y=5/24#

#color(blue)(4x) + 21y = 6#.........equation #(1)#
#color(blue)(4x) - 3y =1#...........equation #(2)#

Solving by elimination:
Subtracting equation #2# from #1#:

#cancelcolor(blue)(4x) + 21y = 6#
#-cancelcolor(blue)(4x) + 3y = -1#

#24y = 5#

#color(green)(y=5/24#

Finding #x# from equation #1#:

#4x + 21y = 6#

#4x = 6 - 21y #

#4x = 6 - 21 * color(green)(5/24 #

#4x = 6 - 105/24 #

#4x = 144/24 - 105/24 #

#4x =39/24 #

#x =39/(24 * 4) #

#color(green)(x =13/32#