How do solve the following linear system?: #5x + y = 9 , -4x + 9y = 9 #?

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Answer 1 · 2016-04-14T09:37:27

The solution for the system of equations is :
#x = 72 / 49 #

# y = 81/49 #

#5x + y = 9#, multiplying by #9#
#45x + color(blue)(9y) = 81#...............equation #(1)#

#-4x + color(blue)( 9y) =9 #...............equation #(2)#

Solving by elimination

Subtracting equation #2# from #1# :

#45x + cancelcolor(blue)(9y) = 81#

#+4x - cancelcolor(blue)( 9y) = -9 #

#49 x = 72#

#x = 72 / 49 #

Finding #y# from equation #1#
#45x + 9y = 81#

# 9y = 81 - 45x #

# 9y = 81 - 45 * ( 72 / 49) #

# 9y = 3969/49 - ( 3240 / 49) #

# 9y = 729 /49 #

# y = 729 /(49 * 9 ) #

# y = 81/49 #