Hey there, future test-day champion.

You know that feeling on the SAT Math section? The clock is ticking, and you’re staring at a problem you know how to solve, but you also know it’s going to take a dozen messy steps. On the digital SAT, where every second counts, efficiency isn’t just nice—it’s a point-scoring strategy.

One of the most common places students lose time is on systems of linear equations. You’ve learned the two main ways to solve them: Substitution and Elimination. But the secret that top scorers know is that they aren’t just two options; they are two different tools for two different types of jobs. Choosing the right tool from the start is the difference between a 30-second solve and a 90-second struggle.

Let’s break down when to use each one.

The Two Tools in Your Toolbox

First, a quick refresher:

• Substitution: This is the “plug-and-play” method. You solve one equation for a single variable (like y =… or x =…) and then substitute that expression into the other equation.
• Elimination: This is the “stack-and-attack” method. You line up the two equations and add or subtract them to make one of the variables completely disappear.

Most students have a favorite method, but relying on just one is like trying to build a house with only a hammer. To be fast, you need to let the problem tell you which tool to pick up.

The Decision Framework: When to Use Substitution

This one is simple. A problem is screaming “Use Substitution!” when:

One of the variables is already isolated (or is super easy to isolate).

If you see an equation that’s already in the form y = 3x + 5 or x = 2y – 1, the test-makers have handed you a gift. They’ve done the first step for you. Just take that expression and plug it directly into the other equation.

Example: y = -3x + 7 2x + 4y = 8

See that y all by itself in the first equation? That’s your green light. Don’t even think about Elimination. Substitute (-3x + 7) for y in the second equation and solve.

The Decision Framework: When to Use Elimination

A problem is begging for Elimination when:

Both equations are in standard form (Ax + By = C), and the variables are neatly lined up.

When you see the x’s, y’s, and equals signs all stacked vertically, your brain should immediately think “Elimination.” The process is even faster if the coefficients for one variable are already the same or opposites.

Example: 4x + 2y = 14 5x – 2y = 13

Look at that beautiful +2y and -2y. They are perfectly lined up and are opposites. This system is tailor-made for Elimination. Just add the two equations together, and the y-terms vanish instantly, leaving you with 9x = 27. It’s clean, it’s fast, and it avoids the messy fractions that substitution might create here.

Putting It Into Practice: A Test-Day Scenario

Let’s look at a typical SAT problem:

A small business owner is buying notebooks and pens. She buys a total of 15 items. Notebooks cost $4 each and pens cost $2 each. If she spent a total of $48, which of the following systems of equations models this situation?

Okay, you set up your system: Let n be notebooks and p be pens.

n + p = 15 4n + 2p = 48

Now, which tool do you grab?

• The Substitution Brain: You could easily turn the first equation into n = 15 – p. This is a solid choice! It’s one simple step to isolate a variable.
• The Elimination Brain: You see the variables are lined up. You could multiply the entire first equation by -2 to get -2n – 2p = -30. Now your +2p and -2p will cancel perfectly when you add the equations.

In this case, both methods are strong contenders. But what if the first equation was 2n + p = 15? Then isolating p is still a one-step move, making Substitution slightly faster. What if the second equation was 4n – p = 48? Then the +p and -p are perfect opposites, making Elimination the clear winner.

The key is to take two seconds to analyze the structure of the system before you start writing. Ask yourself: “Is a variable already alone?” If yes, substitute. If not, “Are the equations lined up neatly?” If yes, eliminate.

Making that quick decision is a habit that separates good math students from great SAT test-takers. Start making it a part of your practice, and watch those systems of equations become a source of fast, easy points.