How to solve functions

Question

How do you solve 5x+2y=10

Answer 1

You can't solve it without another similar equation. The graph of that equation is a straight-line. To solve it, you would need another line which intersects it. The intersection point is the solution.

You can re-write that equation so that you have an expression for either y in terms of x, or x in terms of y:

5x + 2y = 10

Subtract 5x from both sides.

2y = -5x + 10

Divide both sides by 2;

y = -2.5x + 5

You now have y as a function of x. For any given x, you have an expression that provides the corresponding value of x.

You could call that solving for y (in terms of x).

You can also solve for x (in terms of y):

5x + 2y = 10

Subtract 2y from both sides:

5x = -2y + 10

Divide both sides by 5:

x = -0.4y + 2

Your teacher is probably looking for

y = -2.5x + 5

Without saying either "solve for y in terms of x" or "solve for x in terms of y", the problem is poorly stated.

Note:

y = -2.5x + 5

Is a function (of y in terms of x).