Answer: Multiple Solutions
Explanation:
To solve the equation 6x - 2y = 14, we can use algebraic methods to find the values of x and y that satisfy this equation.
Step 1: Simplify the equation if needed. In this case, the equation is already simplified.
Step 2: Solve for x or y. Let's solve for x in terms of y.
- Subtract -2y from both sides of the equation:
6x - 2y - (-2y) = 14 - (-2y)
6x = 14 + 2y
- Divide both sides of the equation by 6 to isolate x:
(6x)/6 = (14 + 2y)/6
x = (14 + 2y)/6
So, x = (14 + 2y)/6.
Step 3: Check for any restrictions. In this case, there are no restrictions.
Step 4: Find possible solutions. We can choose values for y and plug them into the equation to find the corresponding values of x. Let's consider a few examples:
- When y = 0:
x = (14 + 2(0))/6
x = 14/6
x = 7/3
- When y = 2:
x = (14 + 2(2))/6
x = 18/6
x = 3
- When y = -3:
x = (14 + 2(-3))/6
x = 8/6
x = 4/3
So, there are multiple solutions to the equation 6x - 2y = 14, depending on the value of y. The corresponding values of x will vary accordingly.
Hope this helps.