How do you solve #3x – 2y = 26# and #-7x + 3y = -49# using substitution?

1 Answer
Apr 15, 2018

Answer:

#x = 4#
#y =-7#

Explanation:

Solve by simultaneous equations:

#3x - 2y = 26#
#-7x+3y = -49#

Rearrange #3x - 2y = 26# to make #x# the subject of the equation:

#3x = 26 + 2y#
#x = (26 + 2y) / 3#

Substitute the value of #x# into #-7x+3y = -49#:
#-7*((26 + 2y) / 3) + 3y = -49#
#-7*(26/3 + (2y)/3) + 3y = -49#

Multiply out the brackets:
#-182/3 + -(14y)/3 + 3y = -49#

Rearrange and place like terms together:
#-(14y)/3 + 3y = -49 + 182/3#

Simplify and solve for y:

#-(5y)/3 = 35/3#
#-5y = 35/3 *3#
#-5y = 35#
#y = 35 / -5#
#y = -7#

Use value of y to subsitute into any of the two original equations and solve for x:

#3x - 2y = 26#
#3x - 2*(-7) = 26#
#3x + 14 = 26#
#3x = 26 - 14#
#3x = 12#
#x = 12/3#
#x = 4#