How do solve the following linear system?: # x-y=11 , -4x-15y=-1 #?

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Answer 1 · 2016-05-03T12:04:22

The solution for the system of equations is:
#color(green)( x = 166/ 19 #
#color(green)(y = - 43/ 19#

# x - y = 11#, multiplying by #4#

# color(blue)(4x) - 4y = 44#..............equation #(1)#

#color(blue)(- 4x) - 15y = -1 #.......equation #(2)#

Solving by elimination

Adding equations #1# and #2# , eliminates #color(blue)(4x) #

# cancelcolor(blue)(4x) - 4y = 44#
#cancelcolor(blue)(- 4x) - 15y = -1 #

#-19y = 43#

#y = 43/ (-19)#

#color(green)(y = - 43/ 19#

Finding the value of #x# from equation #1# using the value of #y#:

# x - y = 11#

# x = 11 + y#

# x = 11 color(green)(- 43/19 #

# x = 209 / 19 color(green)(- 43/19 #

#color(green)( x = 166/ 19 #