Simplifying · Two Variables · C3

Subtract with two variables.

Subtraction across two variables: combine the xs and the ys with their signs. 6x + 4y − 2x − 5y = 4x − y.

01 / THE IDEA

See it simplify.

See the like terms

Same colour = like terms.

6x
4y
-2x
-5y

All the terms, mixed up.

Watch it simplify

Subtract with two variables

6x + 4y − 2x − 5y: xs → 4x, ys → −y.

1 / 2
6x+4y−2x−5y6x + 4y - 2x - 5y
1

Group like terms

Gather the terms that share the same variable part.

(6x−2x)+(4y−5y)(6x - 2x) + (4y - 5y)
2

Combine

Add the coefficients within each group.

4x−y4x - y
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Simplify it.

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

streak 0
best 0
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— / WHY IT WORKS

The idea underneath.

Signed two-variable collection

Treat each term as a signed coefficient. xs: 6 − 2 = 4. ys: 4 − 5 = −1, i.e. −y. Result 4x − y.

Why it works

Two number lines: one for x-counts, one for y-counts.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

7x + 5y - 4x - 2y

1

Group like terms

Gather the terms that share the same variable part. → (7x - 4x) + (5y - 2y)

2

Combine

Add the coefficients within each group. → 3x + 3y

EX 2medium

12x + 7y - 7x - 3y

1

Group like terms

Gather the terms that share the same variable part. → (12x - 7x) + (7y - 3y)

2

Combine

Add the coefficients within each group. → 5x + 4y

EX 3hard

6x + 6y - 5x - 4y

1

Group like terms

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

2

Combine

Add the coefficients within each group. → x + 2y

04 / COMMON TRAPS

Where students slip.

Trap

4y − 5y = y.

Fix

It is −y; 4 − 5 = −1.

Trap

Letting an x-sign affect a y.

Fix

Each letter has its own signs.

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 7x + 5y - 4x - 2y

Need a hint?
  • Combine the x-coefficients, then the y-coefficients.
  • Watch for negative results.
C2

Simplify 4x + 3y - 2x - 5y

Need a hint?
  • Combine the x-coefficients, then the y-coefficients.
  • Watch for negative results.
C3

Simplify 4x + 2y - 3x - 2y

Need a hint?
  • Combine the x-coefficients, then the y-coefficients.
  • Watch for negative results.
C4

Simplify 5x + 6y - 2x - 2y

Need a hint?
  • Combine the x-coefficients, then the y-coefficients.
  • Watch for negative results.
Apply

Apply (4)

A1

Simplify 12x + 7y - 7x - 3y

Need a hint?
  • Combine the x-coefficients, then the y-coefficients.
  • Watch for negative results.
A2

Simplify 5x + 7y - 4x - 4y

Need a hint?
  • Combine the x-coefficients, then the y-coefficients.
  • Watch for negative results.
A3

Simplify 8x + 4y - 5x - 3y

Need a hint?
  • Combine the x-coefficients, then the y-coefficients.
  • Watch for negative results.
A4

Simplify 7x + 9y - 3x - 3y

Need a hint?
  • Combine the x-coefficients, then the y-coefficients.
  • Watch for negative results.
Extension

Extension (4)

E1

Simplify 6x + 6y - 5x - 4y

Need a hint?
  • Combine the x-coefficients, then the y-coefficients.
  • Watch for negative results.
E2

Simplify 10x + 11y - 5x - 9y

Need a hint?
  • Combine the x-coefficients, then the y-coefficients.
  • Watch for negative results.
E3

Simplify 10x + 12y - 5x - 6y

Need a hint?
  • Combine the x-coefficients, then the y-coefficients.
  • Watch for negative results.
E4

Simplify 14x + 10y - 5x - 4y

Need a hint?
  • Combine the x-coefficients, then the y-coefficients.
  • Watch for negative results.