How do you solve the system of equations #4x + 7y = 9# and #- 2x - 3= y#?

1 Answer
Jim G.
Jul 5, 2017

#(x,y)to(-3,3)#

Explanation:

#4x+7color(red)(y)=9to(1)#

#-2x-3=color(red)(y)to(2)#

#"from " (2)" substitute the value of y into " (1)#

#4x+7(-2x-3)=9larr" distribute"#

#rArr4x-14x-21=9larr" collect like terms"#

#rArr-10x-21=9#

#"add 21 to both sides"#

#-10xcancel(-21)cancel(+21)=9+21#

#rArr-10x=30#

#"divide both sides by - 10"#

#(cancel(-10) x)/cancel(-10)=30/(-10)#

#rArrx=-3#

#"substitute this value into " (2)#

#y=(-2xx-3)-3=3#

#color(blue)"As a check"#

#"substitute values for x and y into " (1)#

#(4xx-3)+(7xx3)=-12+21=9larr" True"#

#"point of intersection "=(-3,3)#
graph{(y+2x+3)(y+4/7x-9/7)=0 [-10, 10, -5, 5]}

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