Solve the following system of equations

x + 4y=6
x= 4-4y

A. The solution is an ordered pair ( , )
B. No Solution

By substitution

Repalce the value of x in first equation:
4.4 y + 4y = 6
8.4y = 6
y = 6/8.4 = 1/1.4
Multiply both numeratoy and denomenator by 5 to get the answer 5/7
y = 5/7
To find x:
Replace y as 5/7 in the first equaton:
x + 4y = 6
x + (4 x 5/7) = 6
x = 6 - 20/7
x = 42/7 - 20/7 = 22/7

x = 22/7; y = 5/7.

sub x = 4 - 4y into the first

4 - 4y + 4y = 6
4 = 6
contradiction, therefore we have no solution

To solve the given system of equations, we can use the method of substitution.

Step 1: Solve one equation for one variable in terms of the other variable.
Let's start with the second equation:
x = 4 - 4y

Step 2: Substitute the expression for that variable in the other equation.
Replace x in the first equation with the expression 4 - 4y:
4 - 4y + 4y = 6

Simplifying this equation, we get:
4 = 6

Step 3: Analyze the result.
The equation 4 = 6 is not true. It means that there is no valid solution that satisfies both equations simultaneously.

Therefore, the correct answer is:
B. No Solution.