SOLUTION: solving systems using substitution x = y + 4 y = x + 4

Question 79727: solving systems using substitution
x = y + 4
y = x + 4
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
x = y + 4
y = x + 4
.
This set of equations has no common solution. Let's try substitution. The top equation
is solved for x. Therefore, you can take the right side of this equation and substitute
it for x in the bottom equation. If you do that the bottom equation becomes:
.
y = (y + 4) + 4
.
The parentheses are just there to show you where the substitution was made. They are
preceded by an implied + sign so you can just erase them to get:
.
y = y + 4 + 4
.
Do the addition on the right side:
.
y = y + 8
.
Just looking at this equation you should see that the right side can't equal the left side,
but you can really see it if you subtract y from both sides. If you do that you get:
.
0 = 8
.
Can't be.
.
What you can do to see the problem is to return to the original equation set and solve the
top equation for y. You can do that by subtracting 4 from both sides to get:
.
x - 4 = y
.
which can be transposed to:
.
y = x - 4
.
So now your equation set is:
.
y = x - 4 and
y = x + 4
.
Both of these equations are in the slope intercept form. In each of the equations
the slope (which is the multiplier of the x term) is +1. That means the slope is the
same for both graphs. The constant term on the right side of each equation is the point
where the graph crosses the y-axis. The graph of the first equation crosses the y-axis
at - 4, and the graph of the second equation crosses the y-axis at +4. Because these
two graphs have the same slope they are separate lines, but they are parallel. That
means they never cross. But for linear equations such as these, for there to be a common
solution, the lines need to cross, and the common solution is the point at which the lines
intersect.
.
Hope this helps you to understand why there is no common solution for this set of equations.
RELATED QUESTIONS
3x-2y=0 x+y=-5 Solving Systems Using... (answered by stanbon)

solving systems by substitution solve each system of equations using the substitution... (answered by mananth)

I need help on solving systems using substitutions. Y=X+4... (answered by jim_thompson5910)

What is the solution for 2y=x+3 and x=y in Solving Systems Using... (answered by rmromero)

solving linear systems using substitution, what is 4x-7y=10 y=x-7 (answered by mananth)

solving by substitution. x+y=4... (answered by swincher4391)

What is the solution for x-y=1 and x=1/2y+2 in Solving Systems Using... (answered by rmromero)

Please help me solve this equation related to solving systems using substitution: x=y... (answered by mananth)

x+3y=4 -x+2y=-4 SOLVING SYSTEMS USING... (answered by Alan3354)