How do solve the following linear system?: #5x + y = 9 , 3x+ 2y - 3 = 0 #?

1 Answer
Jim G.
May 28, 2018

#(x,y)to(15/7,-12/7)#

Explanation:

#5x+y=9to(1)#

#3x+2y-3=0to(2)#

#"rearrange "(1)" expressing y in terms of x"#

#"subtract "5x" from both sides"#

#y=9-5xto(3)#

#"substitute "y=9-5x" into equation "(2)#

#3x+2(9-5x)-3=0#

#3x+18-10x-3=0#

#-7x+15=0#

#"subtract 15 from both sides"#

#-7x=-15#

#"divide both sides by "-7#

#(cancel(-7) x)/cancel(-7)=(-15)/(-7)rArrx=15/7#

#"substitute "x=15/7" in equation "(3)#

#y=9-75/7=63/7-75/7=-12/7#

#"point of intersection "=(15/7,-12/7)#

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