please solve
x+5y=10
-2x-10y=-20
Since the second equation can be obtained from the first (by multiplying both sides by -2), they are not independent and there is no unique solution. There are an infinite number of x,y combinations that are solutions.
To solve this system of equations, we can use the method of elimination.
Step 1: Multiply the first equation by 2 to make the coefficients of "x" in both equations the same (-2x and 2x).
2(x + 5y) = 2(10)
-2x - 10y = -20
Simplifying, we get:
2x + 10y = 20
-2x - 10y = -20
Step 2: Add the two equations together to eliminate the "x" terms.
(2x + 10y) + (-2x - 10y) = 20 + (-20)
Simplifying, we get:
0 = 0
Step 3: The result of the equation is 0 = 0, which means the equation is always true. This indicates that the system of equations is dependent, meaning there are an infinite number of solutions.
In this case, any (x, y) values that satisfy the first equation, x + 5y = 10, will also satisfy the second equation, -2x - 10y = -20. Thus, there is no unique solution to this system of equations.