How do you solve the system of equations #3x - 2y = 13# and #x = - y - 4#?

1 Answer
Jim G.
May 5, 2017

#(1,-5)#

Explanation:

#3color(red)(x)-2y=13to(1)#

#color(red)(x)=-y-4to(2)#

#"Since " (2)" is expressed with x as the subject, we can"#
#"substitute it directly into "(1)" and solve for y"#

#rArr3(-y-4)-2y=13#

#rArr-3y-12-2y=13larr" distributing"#

#rArr-5y-12=13larr" simplifying left side"#

#"add 12 to both sides"#

#-5ycancel(-12)cancel(+12)=13+12#

#rArr-5y=25#

#"divide both sides by - 5"#

#(cancel(-5) y)/cancel(-5)=25/(-5)#

#rArry=-5#

#"substitute this value into "(2)" and evaluate for x"#

#y=-5tox=-(-5)-4=5-4=1#

#color(blue)"As a check"#

Substitute these values for x and y into the left side of ( 1 ) and if equal to the right side then they are the solution.

#"left side "=(3xx1)-(2xx-5)=3+10=13#

#rArr"point of intersection "=(1,-5)#
graph{(y+x+4)(y-3/2x+13/2)=0 [-10, 10, -5, 5]}

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