SOLUTION: Solve the following system of equations. x+4y=5 (1) x=6-4y (2) What is the solution of the system?

Question 163088: Solve the following system of equations.
x+4y=5 (1)
x=6-4y (2)
What is the solution of the system?
Found 2 solutions by joecbaseball, checkley77:
Answer by joecbaseball(37) (Show Source): You can put this solution on YOUR website!
Ok, here is the solution:
There are a few different ways to solve a system of equations. The one I will use is the substitution method, since one of the variables (x) is already isolated in the second equation.
So, since, by the second equation, x = 6 - 4y, we can substitute that value of x into the first equation.
When we do, we get:
(6 - 4y) + 4y = 5
Then 6 - 4y + 4y = 5
Then 6 = 5, which is not true, it is a contradiction, and therefore, this system of equations has no solution!
Good luck !
JoeC
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
x+4y=5
x=6-4y
x+4y=6
x+4y=5 now subtract.
-------------------
0x+0x=1 No solution for x or y.
When plotted these two lines are parallel.
4y=-x+5 or y=-x/4+5/4 (red line)
4y=-x+6 or y=-x/4+6/4 or y=-x/4+3/2 (green line)
(graph 300x200 pixels, x from -5 to 5, y from -3 to 3, of TWO functions -x/4 +5/4 and -x/4 +3/2).

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