X plus 2y plus 3z plus 4s plus 5t equals 87?

Answer 1

You can't add them together because they are not like terms (there are 5 different variables) You can only define each variable in terms of the others.

This is a linear equation in 5 variables, so we can say that the given statement is true if we can solve the equation, that is if we can find values for the variables that satisfy the equation. Solutions are points of the form (x, y, z, s, t) which can exist in 5D. We can say that there are infinitely many solutions.

Let's find 5 solutions:

(87, 0, 0, 0, 0)

(0, 87/2, 0, 0, 0)

(0, 0, 29, 0, 0)

(0, 0, 0, 87/4, 0)

(0, 0, 0, 0, 87/5)

We cannot visualize things in 5D, but sometimes we like to say that these 5 points can determine a hyper-plane there. Each solution set is the intercept for one of the 5 perpendicular axes.