How do you solve the system of linear equations #y=2x-3# and #y=-x+4#?

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Answer 1 · 2016-02-19T11:55:29

The solution for the system of equations is:
#color(blue)(x=7/3#
#color(blue)(y=5/3#

#2x -color(blue)( y) = 3# ............equation #(1)#

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

Solving by elimination:

Subtracting equation #2# from #1#:

#2x -cancelcolor(blue)( y) = 3#
#+x cancelcolor(blue)(+y) = +4#

#3x=7#

#x=7/3#

Finding #y# from equation #1#

#2x - y = 3#

#2x - 3 = y#

#2 xx (7/3) - 3 = y#

#14/3 - 9/3= y#

# y = 5/3#