How do you solve x = y - 8x=y8 and -x - y = 0xy=0 using substitution?

3 Answers
Feb 20, 2017

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 -> 2x =-8 -> x= -4

Hence y=4

Feb 20, 2017

(-4,4)(4,4)

Explanation:

"Given "color(red)(x=y-8)Given x=y8 we can color(blue)"substitute"substitute this directly into the other equation, and solve for y

rArr-(color(red)(y-8))-y=0(y8)y=0

distributing gives.

-y+8-y=0y+8y=0

simplifying.

-2y+8=02y+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"

Feb 20, 2017

Replace x with (y-8) in "–"x-y=0; solve for y.
Use this y-value in either equation to solve for x.

(x,y)=("–"4,4).

Explanation:

Each of these equations represents a line in 2D-space. Solving the system of these two equations means finding all the (x,y) points where the lines cross.

We are given the equations x=y-8 and "–"x-y=0. From the first equation, we have a value for x in terms of y. That is, for the first line, x is always y-8. To see if this line has any points in common with the other line "–"x-y=0, we want to check if an x value of y-8 works for any point on that other line.

So, we substitute x out for y-8 in the second equation:

"      ""–"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 x will be y-8, and that point occurs when y=4.

The only thing left to do is to find the x-value for this point. To do that, we can plug y=4 into either of our line equations and solve for x. (Since y=4 is where the lines cross, both equations will have the same x-value for that y).

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 x-value, as we'd expect.)

So our solution for the system is (x,y)=("–"4, 4).

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