Solve the following system of equations.
x+4y=5
x=6-4y
What is the solution of the system?
a) The solution of the system is ___? (TYPE AN ORDERED PAIR)
b) There is no solution
1(6-4y) + 4y = 5
6-4y + 4y = 5
-4y + 4y = 5-6
0 = -1
No solution
To solve the system of equations, we can use the method of substitution or elimination. In this case, let's use the substitution method.
1. Start with the first equation:
x + 4y = 5
2. Solve the second equation for x:
x = 6 - 4y
3. Substitute the value of x from the second equation into the first equation:
(6 - 4y) + 4y = 5
4. Simplify the equation:
6 - 4y + 4y = 5
6 = 5
5. Since 6 does not equal 5, we have a contradiction in the equation. This means that the system of equations has no solution.
b) Therefore, the solution to the system of equations is: There is no solution.