solve the following system by the substitution method 4x+y=6 y=6-4x
To solve the system of equations using the substitution method, we need to substitute one equation into the other and solve for the remaining variable.
Given:
1) 4x + y = 6
2) y = 6 - 4x
Substitute equation 2) into equation 1) for y:
4x + (6 - 4x) = 6
Simplify the equation:
4x + 6 - 4x = 6
The x-terms cancel out.
6 = 6
The equation is true, which means the system of equations is consistent and dependent. This means there are infinitely many solutions.
To find the solutions, we can choose a value for x and substitute it back into either of the original equations to find the corresponding y-value.
Let's choose x = 0:
Using equation 2), substitute x = 0:
y = 6 - 4(0)
y = 6 - 0
y = 6
So one solution to the system is (x, y) = (0, 6).
Now let's choose x = 1:
Using equation 2), substitute x = 1:
y = 6 - 4(1)
y = 6 - 4
y = 2
So another solution to the system is (x, y) = (1, 2).
We can continue this process to find infinitely many solutions to the system.