Simplifying · Two Variables · C2

Collect each letter.

With two variables, collect each letter separately. 2x + 3y + 5x = 7x + 3y. Run through the xs, then the ys.

01 / THE IDEA

See it simplify.

See the like terms

Same colour = like terms.

2x
3y
5x

All the terms, mixed up.

Watch it simplify

Collect each letter

2x + 3y + 5x: xs give 7x, ys give 3y → 7x + 3y.

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2x+3y+5x2x + 3y + 5x
1

Group like terms

Gather the terms that share the same variable part.

(2x+5x)+3y(2x + 5x) + 3y
2

Combine

Add the coefficients within each group.

7x+3y7x + 3y
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Simplify it.

Type the simplest form (e.g. 6x + 5). Use ^ for powers.

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— / WHY IT WORKS

The idea underneath.

One letter at a time

Sweep up the x-terms, then the y-terms. 2x + 3y + 5x = 7x + 3y. Order: x-terms, then y-terms.

Why it works

Two piles: an x-pile and a y-pile.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

4x + 3y + 3x + 4y

1

Group like terms

Gather the terms that share the same variable part. → (4x + 3x) + (3y + 4y)

2

Combine

Add the coefficients within each group. → 7x + 7y

EX 2medium

5x + 4y + 6x + 3y

1

Group like terms

Gather the terms that share the same variable part. → (5x + 6x) + (4y + 3y)

2

Combine

Add the coefficients within each group. → 11x + 7y

EX 3hard

10x + 9y + 7x + 5y

1

Group like terms

Gather the terms that share the same variable part. → (10x + 7x) + (9y + 5y)

2

Combine

Add the coefficients within each group. → 17x + 14y

04 / COMMON TRAPS

Where students slip.

Trap

Mixing xs and ys.

Fix

Keep them in separate piles.

Trap

Forgetting a y-term.

Fix

Collect every letter.

05 / QUIZ

Test yourself.

The Test

12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.

0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).
Core

Core (4)

C1

Simplify 4x + 3y + 3x + 4y

Need a hint?
  • Collect the x-terms, then the y-terms.
  • Keep the piles separate.
C2

Simplify 6x + 3y + 2x + 3y

Need a hint?
  • Collect the x-terms, then the y-terms.
  • Keep the piles separate.
C3

Simplify 4x + 6y + 3x + 3y

Need a hint?
  • Collect the x-terms, then the y-terms.
  • Keep the piles separate.
C4

Simplify 6x + 3y + 4x + 2y

Need a hint?
  • Collect the x-terms, then the y-terms.
  • Keep the piles separate.
Apply

Apply (4)

A1

Simplify 5x + 4y + 6x + 3y

Need a hint?
  • Collect the x-terms, then the y-terms.
  • Keep the piles separate.
A2

Simplify 5x + 3y + 5x + 6y

Need a hint?
  • Collect the x-terms, then the y-terms.
  • Keep the piles separate.
A3

Simplify 3x + 8y + 5x + 3y

Need a hint?
  • Collect the x-terms, then the y-terms.
  • Keep the piles separate.
A4

Simplify 6x + 6y + 9x + 5y

Need a hint?
  • Collect the x-terms, then the y-terms.
  • Keep the piles separate.
Extension

Extension (4)

E1

Simplify 10x + 9y + 7x + 5y

Need a hint?
  • Collect the x-terms, then the y-terms.
  • Keep the piles separate.
E2

Simplify 5x + 4y + 9x + 9y

Need a hint?
  • Collect the x-terms, then the y-terms.
  • Keep the piles separate.
E3

Simplify 10x + 8y + 10x + 8y

Need a hint?
  • Collect the x-terms, then the y-terms.
  • Keep the piles separate.
E4

Simplify 4x + 4y + 5x + 4y

Need a hint?
  • Collect the x-terms, then the y-terms.
  • Keep the piles separate.