Eliminate the Confusion: Solving Systems of Equations the Easy Way

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So anyway, solving systems of equations might sound intimidating, but once you get the hang of elimination, it’s actually one of the easiest ways to find where two lines cross. If test anxiety or SAT anxiety makes these problems seem overwhelming, don’t worry—I’ve got you covered with a step-by-step breakdown.

Let’s dive into the elimination method and see why it’s such a powerful tool.

What Is the Elimination Method?

When solving a system of equations, you’re looking for the point (x,y) where both equations are true at the same time. Instead of graphing, elimination allows us to add or subtract the equations to cancel out one of the variables, making it easier to solve for the other.

Think of it like a magic trick—you make one variable disappear and solve for the other!

Step 1: Line Up the Equations

Step 2: Make One Variable Cancel Out

Step 3: Add the Equations

Step 4: Solve for the First Variable

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Step 5: Solve for the Second Variable

Visualizing the Solution

The elimination method finds the exact point where the two lines cross. If we were to graph them, the two lines would intersect at…

Here’s a visual representation:

Practice Problem

Try solving this one on your own:3x+4y=18…and…6x−2y=6

Follow these steps:

  1. Multiply one equation if needed to make a variable cancel out.
  2. Add or subtract to eliminate that variable.
  3. Solve for the remaining variable.
  4. Plug it back into one of the original equations.

What solution do you get?

Test Anxiety Tip: Stick to the Process

If SAT anxiety makes elimination problems feel stressful, just focus on following the steps:

  1. Line up the equations in standard form.
  2. Multiply one (or both) equations if needed to make a variable cancel.
  3. Add or subtract to eliminate a variable.
  4. Solve for the remaining variable.
  5. Substitute back in to find the second variable.

By sticking to this system, you’ll always know what to do next!

Final Thoughts

Solving systems of equations with elimination is one of the fastest and most efficient ways to find solutions. With a little practice, you’ll start seeing these problems as easy points on the SAT.

Keep checking back on this blog for more helpful math tricks, and keep practicing—you’ve got this!