How do you solve the system of equations: x + 2y = 7, 2x + y = 8?

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Answer 1 · 2015-08-14T11:50:41

The solutions are
#color(blue)(x=3,y=2#

#x + 2y = 7#, multiplying this equation by #2#
#color(blue)(2x )+ 4y = 14#,.......equation #1#

# color(blue)(2x) + y = 8#....equation #2#

Solving by elimination .

Subtracting equation #2 # from #1# to eliminate #color(blue)(2x#

#cancel(color(blue)(2x ))+ 4y = 14#
# -cancel(color(blue)(2x)) - y =- 8#

#3y=6#
#color(blue)(y=2#

Now, we find #x# by substituting #y# in equation #1#
#x + 2y = 7#

#x = 7-2y#

#x=7-2*2#
#x=7-4#
#color(blue)(x=3#