Systems of Equations are extremely prevalent in math competitions. They may sound complicated, but systems of equations are straightforward with adequate practice. Let’s look at an example:

• Now, my dad is triple my age. In ten years, he will be double my age. How old am I?

This problem may look simple, but you may not know how to start. It is always a good strategy to assign variables to a problem and work from there. We will use D to represent the dad’s age now and C to represent the child’s age now. Let’s write a System of Equations:

Now: D = 3C

In 10 years: D + 10 = 2(C + 10)

Take a moment to understand these two equations. Now, there are two ways that we can solve this system: substitution and elimination. Let’s try using substitution first. Substitution is where we plug in a variable from one equation into the corresponding variable in the other equation. Let’s try it!

From the second equation: D = 2(C + 10) - 10. Let’s plug that into D in the first equation:

2(C + 10) - 10 = 3C. Let’s make that neater: 2C + 10 = 3C.

Subtracting 2C from both sides, we get: 10 = C. This is our answer! The child in this problem is 10 years old!

Now, let’s try solving the problem using elimination. Elimination is where we try to cancel out the variable by adding or subtracting whole equations! It may sound complicated, but it can be useful. Let’s try it!

Since D has the same coefficient in both equations, we can eliminate D. To do this, let’s subtract the first equation from the second equation. We can split it up by evaluating the left side and right side separately, to make it easier for us.

D + 10 - D = 10, so the left sides evaluate to 10.

The right sides become 2(C + 10) - 3C. Cleaning it up, we get 2C + 20 - 3C, or 20 - C.

So, our final equation is: 10 = 20 - C. Rearranging, we get C = 10, which is the same answer we got previously!

With more practice, you will improve your skills with writing equations, simplifying equations, determining whether to use substitution or elimination, and solving Systems of Equations problems. This is an important skill to master to succeed in math contests.