How do you solve #3y = -(1/2)x + 2# and #y = -x + 9# using substitution?

2 Answers
Apr 2, 2018

Answer:

#y= -1#

#x= 10#

Explanation:

Substitute #y= -x + 9# in equation 1: #3y= -0.5x + 2#

#3(-x + 9) = -0.5x + 2#

#-3x + 27 = -0.5x + 2#

#-3 + 0.5 = 2 - 27#

#-2.5x = -25#

The minus signs cancel each other

#2.5x = 25#

#x = 10#

Now substitute #x = 10# in equation 2: #y = -x + 9#

#y = -10 + 9#

#y = -1#

Apr 2, 2018

Answer:

#x = 10; y = -1 #

Explanation:

Substituting a formula into another essentially means, to set one formula equal to a variable and then inserting the formula into the other formula. Though this might seem complicated, this can be done easily with these equations:
#3y = ((-1)/2)x + 2 #
#y = -x + 9#
#3(-x+9) = ((-1)/2)x + 2 #
#-3x + 27 = ((-1)/2)x + 2#

Now rearrange the equation to collect like terms on either sides.
1) multiply both sides of the equation by 2 to simplify the situation.
#-6x + 54 = -1x + 4#

2) add #1x# to both sides, to eliminate the x on the right side
#-6x (+ x) + 54 = -1x (+ x) + 4#
#-5x + 54 = 4#

3) subtract #54# from both sides
#-5x + 54 (- 54) = 4 (- 54)#
#-5x = -50#

4) now divide both sides of the equation by #-5#
#(-5x)/-5 = (-50)/-5#
#x = 10#

Now just use this value in one of the initial equations.
#y = -x + 9#
#y = -(10) + 9#
#y = -1#