The equation given is 3x + 4y = 8. To find the solutions, we need to express it in terms of y or x.
Rearranging the equation for y:
- 4y = 8 – 3x
- y = (8 – 3x) / 4
Now, we can substitute different values of x into this equation to see what pairs (x, y) satisfy the equation. Here are a few examples:
- If x = 0, then y = (8 – 3(0)) / 4 = 2, so one solution is (0, 2).
- If x = 4, then y = (8 – 3(4)) / 4 = -1, so another solution is (4, -1).
- If x = 2, then y = (8 – 3(2)) / 4 = 1, so another solution is (2, 1).
To summarize, the solutions that apply to the equation 3x + 4y = 8 include the points (0, 2), (4, -1), and (2, 1). You can continue substituting different values to find more solutions, as this line represents all possible solutions in the (x, y) coordinate plane.
In conclusion, select all the points that you have derived or calculated using the above method, and those will be your solutions to the equation!