How do you solve the following system: #10y=42+2x , y= 3/4x+3 #?

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Answer 1 · 2016-04-06T06:46:35

#x=24/11#
#y=51/11#

#10y=42+2x" (1)"#

#"expand the second equation by 10"#

#y=3/4x+3" (2)"#

#color(red)10*y=color(red)10*(3/4x+3)#

#10y=30/4x+30" (3)"#

#"so left side of the equations (1) and (3)are equal"#

#"we can write:"#

#42+2x=30/4x+30#

#2x-30x/4=30-42#

#(8x-30x)/4=-12#
#-22x=-4*12#

#22x=48" "x=48/22#
#x=24/11#

#" now use the equation (1)"#

#10y=42+2(24/11)#

#10y=42+48/11#

#10y=(462+48)/11#

#y=(51cancel(0))/(11cancel(0))#

#y=51/11#