Lesson 1 — Intro to Two-Variable Linear Equations

An equation like ax + by = c, y = mx + b, or x = k is linear in two variables. A solution is any ordered pair (x, y) that satisfies the equation when substituted.

What counts as a solution?

For y = 2x + 3, the pair (2, 7) is a solution because substituting x = 2 gives y = 2(2) + 3 = 7, which matches y = 7.

For 2x + y = 1, the pair (−1, 4) is not a solution because 2(−1) + 4 = −2 + 4 = 2 ≠ 1.

For x = 3, a vertical line, the pair (3, 5) is a solution because x = 3 holds, regardless of y.

For 3x − 2y = 6, the pair (0, −3) is a solution because 3(0) − 2(−3) = 0 + 6 = 6.

Key idea

Ordered pairs (x, y) Substitute to verify Solutions form a line

Practice checking if a point satisfies a linear equation by substituting x and y.

Solution Checker (sandbox)

Type your equation ✍️ (e.g., y=2x+3, 2x+y=7, or x=3)

x value

y value

Computed left side

Enter an equation and a point (x, y). We’ll show if it lands on the line.

Try it — Test your understanding

Question 1 of 5

Is (x, y) = (2, 7) a solution to y = 2x + 3?

More practice (unlocks as you answer correctly)

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