Final answer:
To complete the missing value in the solution to the equation 2x+3y=5x−y, we need to solve for x and y. There are infinitely many solutions to the equation, so any value of y will complete the missing value in the solution.
Step-by-step explanation:
To complete the missing value in the solution to the equation 2x+3y=5x−y, we need to solve for x and y. One approach is to combine like terms on both sides of the equation:
2x + 3y = 5x - y
2x - 5x = -y - 3y
-3x = -4y
x = (4y)/3
Now, we can substitute x into the equation to find a value for y:
2((4y)/3) + 3y = 5((4y)/3) - y
To simplify, we can multiply through by 3 to remove the fractions:
8y + 9y = 20y - 3y
17y = 17y
Since 17y is equal to 17y for all values of y, there are infinitely many solutions to the equation. Therefore, any value of y will complete the missing value in the solution.
So, the missing value in the solution to the equation is any value of y, represented as (__, 0).