Final answer:
To find a point on the line 2x + y = 8 that is equidistant from the coordinate axes, we need to solve the equation and substitute the coordinates into the equation of being equidistant from the axes. The point (8/3, 8/3) satisfies this condition.
Step-by-step explanation:
To find a point on the line 2x + y = 8 that is equidistant from the coordinate axes, we need to find the coordinates (x, y) that satisfy this equation. Let's start by solving the equation for y by subtracting 2x from both sides: y = 8 - 2x. Now, we can substitute y = 8 - 2x into the equation of being equidistant from the coordinate axes. The distance from a point (x, y) to the x-axis is y, and the distance from (x, y) to the y-axis is x. So our equation becomes: y = x. Substituting y = 8 - 2x, we get: 8 - 2x = x. Simplifying this equation, we get: 3x = 8. Solving for x, we find that x = 8/3. Substituting this value of x into y = 8 - 2x, we get: y = 8 - 2(8/3) = 8 - 16/3 = 24/3 - 16/3 = 8/3. Therefore, the point on the line 2x + y = 8 that is equidistant from the coordinate axes is (8/3, 8/3).