How do you solve the system of equations #y= x - 1# and #y = - 5x - 13#?

1 Answer
Jim G.
May 22, 2017

#(-2,-3)#

Explanation:

#color(red)(y)=x-1to(1)#

#color(red)(y)=-5x-13to(2)#

#"both equations express y in terms of x and so we can"#
#"equate the right sides"#

#rArrx-1=-5x-13#

#"add 5x to both sides"#

#x+5x-1=cancel(-5x)cancel(+5x)-13#

#rArr6x-1=-13#

#"add 1 to both sides"#

#6xcancel(-1)cancel(+1)=-13+1#

#rArr6x=-12rArrx=-2#

#"substitute this value into either " (1)" or " (2)#

#rarry=-2-1=-3larr" substituted in " (1)#

#rArr"point of intersection "=(-2,-3)# graph{(y-x+1)(y+5x+13)=0 [-12.66, 12.65, -6.33, 6.33]}

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