What is #y# and #x# when #y= 2x-11# and #y= x- 8# ?

2 Answers
Apr 5, 2017

Answer:

x = + 3 y = -5

Explanation:

One way to solve the problem is to subtract the two equations from each other.

# y = 2x - 11 - (y = x - 8 )#

# y-y = 0#
#2x - x = x#
# - 11 -( -8) = -3#

so # y = 2x - 11 - ( y = x -8) = { 0 = x - 3}#

Solving for #0 = x -3# add 3 to both sides giving

# 0 + 3 = x -3 + 3# so

# +3 = x #

now put the value of +3 into either equation and solve for y

# y = +3 -8#

# y = -5#

To check put these values into the second equation

# -5 = 2(+3) - 11#

#-5 = +6 -11#

# -5 = -5 check

x = +3 y = -5

Apr 5, 2017

Answer:

#color(red)(y=-5,x=3#

Explanation:

#y=2x-11# ------(1)

#y=x-8# ---------(2)

#(2) xx 2#

#2y=2x-16# ------(3)

#(1)-(3)#

#-y=5#

#color(red)(y=-5#

substitute #color(red)(y=-5# in (2)

#color(red)(-5)=x-8#

#x-8=-5#

#x=-5+8#

#color(red)(x=3#

substitute# color(red)(y=-5,x=3# in (1)

#color(red)(-5)=2(color(red)3)-11#

#-5=6-11#

#-5=-5#