Solve by the elimination method.
4x +5y=1
8x +10y=2
What is the solution of the system? N
Type an ordered pair. Type an integer or a fraction. Type N if there is no solution. Type I if there are infinitely many solutions.
The equations are really the same. One can be derived from the other. There are infinitely many solutions. So, Type "I"
I don't see what ordered pairs and integers or fractions have to do with the problem.
If x = 1/4, y = 0. How's that for an ordered pair?
To solve the system of equations using the elimination method, we need to eliminate one variable by adding or subtracting the equations. In this case, let's eliminate the variable "x".
The given equations are:
1) 4x + 5y = 1
2) 8x + 10y = 2
To eliminate the variable "x", we can multiply equation (1) by 2 and equation (2) by -1, so that when we add them together, the "x" terms will cancel out:
Multiply equation (1) by 2:
2(4x + 5y) = 2(1)
Simplifying, we get:
8x + 10y = 2
Multiply equation (2) by -1:
-1(8x + 10y) = -1(2)
Simplifying, we get:
-8x - 10y = -2
Now, let's add the modified equations together:
(8x + 10y) + (-8x - 10y) = 2 + (-2)
Simplifying, we get:
0 = 0
The result is 0 = 0, which is always true. This means that the two equations are dependent, and there are infinitely many solutions. In other words, the two equations represent the same line, so any point on that line will satisfy both equations.
Thus, the solution to the system of equations is "I" for infinitely many solutions.