Linear Equations: The 80/20 Strategy

Linear equations account for roughly a third of SAT Math points. The good news: they follow a small number of repeating patterns.

The three patterns

1. Solve for x — isolate the variable. Watch for questions that ask for an expression (like 3x + 2) rather than x itself. The SAT loves this trap.
2. Interpret the parts — in y = mx + b word problems, the slope m is always a rate of change and b is always a starting value.
3. Count the solutions — one solution (different slopes), no solutions (same slope, different intercept), infinite solutions (same line).

Worked example

If 3(x - 2) = 12 - 3x, what is the value of 6x?

Distribute: 3x - 6 = 12 - 3x → 6x = 18.

Notice you never need x alone. The answer is 18 — and solving for x first wastes 15 seconds. On the SAT, always check what the question actually asks for before you start solving.

Drill checklist

• Can you spot "solve for the expression" traps?
• Can you interpret slope and intercept in context in under 20 seconds?
• Do you know the three solution-count cases cold?