How do you solve x = y - 8x=y−8 and -x - y = 0−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)Given x=y−8 we cancolor(blue)"substitute"substitute this directly into the other equation, and solve for y
rArr-(color(red)(y-8))-y=0⇒−(y−8)−y=0 distributing gives.
-y+8-y=0−y+8−y=0 simplifying.
-2y+8=0−2y+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]}