Solve the system of equations using substitution.
2x−8y
=
2
x+4y
=
0
What is the solution? Select the correct choice below and fill in any answer boxes in your choice.
A.
m (Type an ordered pair.)
B.
There are infinitely many solutions.
C.
There is no solution.
2x-8y=0
x=4y
second equation
x+4y=0
4y+4y=0
y is zero, which means 0,0 is the solution
To solve the system of equations using substitution, we need to solve one equation for one variable and then substitute that expression into the other equation.
Let's solve the second equation for x:
x + 4y = 0
Subtract 4y from both sides:
x = -4y
Now we can substitute this expression (-4y) for x in the first equation:
2x - 8y = 2
Replace x with -4y:
2(-4y) - 8y = 2
Simplify:
-8y - 8y = 2
-16y = 2
Divide both sides by -16:
y = -2/16
Simplify:
y = -1/8
Now we can substitute this value of y back into one of the original equations to find the value of x. Let's use the second equation:
x + 4y = 0
Substitute y = -1/8:
x + 4(-1/8) = 0
x - 1/2 = 0
Add 1/2 to both sides:
x = 1/2
So the solution to the system of equations is (x, y) = (1/2, -1/8).
Therefore, the correct choice is A. m = (1/2, -1/8).