Solve this system using elimination. If a single solution exists, write the solution as an ordered pair. Your answer will be an ordered pair, no solution, or infinitely many solutions
2x-y=0
3x+y=5
Add the two equations.
2x-y=0
3x+y=5
5x = 5
Solve for x, then y.
To solve this system of equations using elimination, we need to eliminate one variable to make the equations easier to solve. In this case, we can eliminate the variable "y" by adding the two equations together.
First, we will multiply the second equation by 2 to make the coefficients of "y" (1 and -1) the same and opposite in sign in both equations.
The original equations are:
1) 2x - y = 0
2) 3x + y = 5
By multiplying the second equation by 2, we get:
3) 6x + 2y = 10
Now, we can add equation 1 and equation 3 to eliminate the variable "y":
2x - y + 6x + 2y = 0 + 10
8x = 10
x = 10/8
x = 5/4 or 1.25
To find the value of "y," we can substitute the value of "x" into either of the original equations. Let's use equation 1:
2(5/4) - y = 0
10/4 - y = 0
5/2 - y = 0
-y = -5/2
y = 5/2 or 2.5
Therefore, the solution to the system of equations is (x, y) = (5/4, 5/2), or as an ordered pair, (1.25, 2.5).