How do you solve x+2y=5 and 2x-3y=-4?

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Answer 1 · 2016-01-21T17:16:08

If P is the point where the two graphs cross then;

#color(purple)(=> P_("crossing point") = (x,y)->(0.7,1.8) ->(7/10,9/5)#

Given:
#color(brown)(x+2y=5)#................................(1)
#color(brown)(2x-3y=-4)#........................(2)

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Using short cut methods: (jumping steps)

#color(blue)("Making y the dependant variable:")#
#y=-x+5/2....................(1_a)#
#y=2/3x+4/3......................(2_a)#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("To determine the value of "x)#

By substitution we can equate equation #(1_a)# to equation #(2_a)# through #y# giving:

#-x+5/2=y=2/3x+4/3#

Collecting like terms

#2/3x+x=5/2-4/3#

#5/3x= (15-8)/6#

#color(blue)(x=7/6xx3/5=7/10)#...........................(3)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("To determine the value of "y)#

Substitute equation (3) into equation #(1_a)#. The easier of the two!

#y=-7/10+5/2 #

#y= (25-7)/10#

#y=18/10 = 9/5#

#color(blue)(y=9/5)#

Tony B

Note: #y=9/5 = 1.8" and "x=7/10=0.7#

#=> P_("crossing point") = (x,y)->(0.7,1.8) #