Final answer:
To find the missing value in the equation 2x+3y=5x-y, we simplify and rearrange the terms to get -3x + 4y = 0, suggesting that the missing value is a) 0.
Step-by-step explanation:
To complete the missing value in the solution to the equation 2x+3y=5x−y, let's first simplify the terms to isolate one of the variables. We can move all terms involving x to one side of the equation and all terms involving y to the other side.
Step 1: Subtract 5x from both sides of the equation:
2x + 3y - 5x = 5x - 5x - y
-3x + 3y = -y
Step 2: Now add y to both sides of the equation:
-3x + 3y + y = -y + y
-3x + 4y = 0
Step 3: We observe that there is no constant term on the right side of the equation, indicating that the x-intercept is 0 when y is 0. Similarly, the y-intercept is also 0 when x is 0 since the equation can be written as y = (3/4)x.
Therefore, the missing value that completes this equation would be a) 0.