Solve the system of equations:
*Remember no spaces in your answer (#,#), type infinite or type none.
{x+2y=4
{y=-1/2x+2
The given system of equations is:
1) x + 2y = 4
2) y = -1/2x + 2
To solve this system, we can use the substitution method or the elimination method. Here, we will use the substitution method.
Let's substitute the value of y from equation 2) into equation 1):
x + 2(-1/2x + 2) = 4
x - x + 4 = 4
4 = 4
This equation implies that 4 = 4, which is true. This means that equation 1) is true for all values of x and y. Therefore, the system of equations is dependent, and there are infinitely many solutions.
So, the solution to the system of equations is infinite.