How do you solve each system of equations and then check the answer algebraically? 11) -6x+3y=33 -4x+y=16 12)2y=5x-1 x+y=-1

1 Answer
Jim G.
Jan 11, 2018

#"see explanation"#

Explanation:

#(11)#

#-6x+3y=33to(1)#

#-4x+y=16to(2)#

#"from "(2)color(white)(x)y=16+4xto(3)#

#color(blue)"Substitute "y=16+4x" in equation "(1)#

#-6x+3(16+4x)=33#

#rArr-6x+48+12x=33#

#rArr6x+48=33#

#"subtract 48 from both sides"#

#6xcancel(+48)cancel(-48)=33-48#

#rArr6x=-15#

#"divide both sides by 6"#

#(cancel(6) x)/cancel(6)=(-15)/6#

#rArrx=-15/6=-5/2#

#"substitute this value in equation "(3)#

#rArry=16+(4xx-5/2)=16-10=6#

#rArr(x,y)to(-5/2,6)#

#color(blue)"As a check"#

#"substitute the solution into either of the 2 equations"#

#(2)to(-4xx-5/2)+6=10+6=16larr" True"#

#"this confirms that "(-5/2,6)" is the solution"#

#(12)#

#"the solution is "(x,y)to(-1/7,-6/7)#

#"this is done in exactly the same way as 11"#

#"you may wish to try it for yourself"#

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