How do you solve the following system of equations?: #13x+3y=16, 17x-y=19#?

1 Answer
Dec 22, 2015

Answer:

The solution for the system of equations is:

#color(blue)(x=73/64#

#color(blue)(y=25/64#

Explanation:

#13x + color(blue)(3y)=16#........equation #(1)#

#17x - y=19#, multiplying this equation by #3#
#51x - color(blue)(3y)=57#..........equation #(2)#

Solving by elimination:

Adding equations #1# and #2#

#13x +cancel color(blue)(3y)=16#

#51x - cancelcolor(blue)(3y)=57#

#64x=73#

#color(blue)(x=73/64#

Finding #y# by substituting #x# in equation #2#

#17x - y=19#

#17x - 19=y#

#17xx color(blue)(73/64)- 19=y#

#(1241/64)- (19xx64)/64=y#

#(1241/64)- (1216)/64=y#

#(25/64)=y#

#color(blue)(y=25/64#