Do you need to add or subtract the equations #5x+7y=-31# and #5x-9y=17# to solve the system?

1 Answer
May 19, 2018

Answer:

See answer below

Explanation:

Given: #5x + 7y = -31; " and " 5x -9y = 17#

Since both equations have a #5x#, subtract one from the other to eliminate the #x# terms:

#" "5x + 7y = -31#
#ul(-(5x -9y = " "17" "))#
#" " 16y = -48; " "y = -48/16 = -3#

Substitute this value for #y# in either of the equations to find the value of #x#:

#5x +7(-3) = -31#

#5x -21 = -31#

Add #21# to both sides: #" "5x = -31 + 21 = -10#

#x = -10/5 = -2#

Check your answer by substituting both #x# and #y# into the other equation:

#5(-2) - 9(-3) = 17#

#-10 +27 = 17#, which is TRUE

Solution: is a point (-2, -3)
which is the intersection point common to both lines