How do you solve the system of linear equations #2x + 5y = 8# and #-3x + y = 5#?

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Answer 1 · 2016-05-10T08:12:36

The solution for the system of equations is
#color(blue)(x = -1 , y = 2 #

#2x + color(green)(5y) = 8#........equation #(1)#

#-3x + y = 5#, multiplying by #5#
#-15x + color(green)(5y) = 2 5#.......equation #(2)#

Solving by elimination:

Subtracting equation #2# from #1#:

#2x + cancelcolor(green)(5y) = 8#
#+15x - cancelcolor(green)(5y) = -2 5#

#17x = -17#

#x = (-17) / 17#

#color(blue)(x = -1#

Finding #y# from equation #2#

#-3x + y = 5#

# y = 5 + 3x#

# y = 5 + 3 * (-1) #

# y = 5 - 3 #

#color(blue)(y =2#

The solution for the system of equations is
#color(blue)(x = -1 , y = 2 #