How do you solve the system of linear equations # x + 2y = 7# and #2x - 3y = -5#?

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Answer 1 · 2016-03-01T18:25:29

The solution for the system of equations is:
#color(blue)(x=11/7#

#color(blue)(y= 19/7#

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

#color(blue)(2x)- 3y=-5#.....equation #(2)#

Solving by elimination

Subtracting equation #2# from #1#

#cancelcolor(blue)(2x)+ 4y=14#

#-cancelcolor(blue)(2x) + 3y= 5#

#7y =19#

#color(blue)(y= 19/7#

Finding #x# from equation #1#:
#x+ 2y=7#

#x+ 2xx19/7=7#

#x+ 38/7=7#

#x=7 - 38/7#

#x=49/7 - 38/7#

#color(blue)(x=11/7#