Algebra

x - y = 3

Step-by-step solution with explanation

Final Answer

Infinitely many solutions: every pair where . Examples: , , . The solution set is the line .

Step-by-step solution

1

Understand what this equation means

This is one equation with two variables. That means there are infinitely many solutions — any pair (x, y) that makes the difference equal 3 works.
2

Solve for x in terms of y

Add y to both sides. Now x is written using y, so we can pick any value of y and find the matching x.
3

Solve for y in terms of x

Subtract x from both sides, then multiply by -1. This lets us go the other way — pick any x and find y.
4

List example solution pairs

Plug in any number for x (or y), then use the formula to get the other value. Every point on the line is a valid solution.
5

Describe the full solution set

The complete solution is an infinite set of ordered pairs. On a graph, this is a straight line with slope 1 and y-intercept -3.

Understanding this problem

Learning Insight

One linear equation with two unknowns is called 'underdetermined.' You need at least as many independent equations as unknowns to get a single unique solution. With just one equation, the solution is an entire line of points, not just one point.

Quick Tip

Remember 'one equation, one unknown = one answer; one equation, two unknowns = infinite answers (a line).' If you see a second equation added later, use substitution: plug x = y + 3 straight into it.

Common Mistake

Students often write only one solution like (3, 0) and stop, forgetting that infinitely many pairs satisfy the equation. Always check how many unknowns vs. equations you have before assuming a unique answer.