# How do you solve #x = y - 8# and #-x - y = 0# using substitution?

##### 3 Answers

x= -4 , y= 4

#### Explanation:

From the second equation -x-y=0, it is y=-x. Now substitute this in the first equation ,

x= -x-8

Hence y=4

#### Explanation:

#"Given "color(red)(x=y-8)# we can#color(blue)"substitute"# this directly into the other equation, and solve for y

#rArr-(color(red)(y-8))-y=0# distributing gives.

#-y+8-y=0# simplifying.

#-2y+8=0# subtract 8 from both sides of the equation.

#-2ycancel(+8)cancel(-8)=0-8#

#rArr-2y=-8# To solve for y, divide both sides by - 2

#(cancel(-2) y)/cancel(-2)=(-8)/(-2)#

#rArry=4# To find x, substitute y = 4 into

#x=y-8#

#y=4tox=4-8=-4#

#rArr(-4,4)" is the solution"#

Replace

Use this

#### Explanation:

Each of these equations represents a line in 2D-space. Solving the system of these two equations means finding all the

We are given the equations

So, we substitute

#" ""–"x" "-y=0#

#"–"(y-8)-y=0#

#" ""–"y+8" "-y=0#

#" –"2y="–"8#

#" "y=4#

So yes—there is a point on the second line where

The only thing left to do is to find the

Using the first equation, we get:

#x=y-8#

#x=4-8#

#color(white)x="–"4#

(Or, using the second equation, we get

#"–"x-y=0#

#"–"x-4=0#

#"–"x" "=4#

#" "x="–"4#

which gives the same

So our solution for the system is

graph{(x-y+8)(x+y)=0 [-12.17, 7.83, -2.76, 7.24]}