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Equations & Systems

Solve linear equations and 2-variable / 3-variable systems mentally using Cramer's rule.

Linear: isolate x. 2-variable: read D from x,y, D_x from -det(y,b), and D_y from det(x,b). 3-variable uses the in-place signs +, -, +.

Visual Methods

Equations approach board showing one variable, two variable, and three variable blocks
1Approach
Linear equation board for 3x plus 7 equals 22
2Linear Equations
Cramer in-place step D uses x and y columns
3Cramer's Rule - 2 Variables
Cramer in-place normal case with x equals 3 and y equals 2
4Cramer In Place
3-variable Cramer Dx sign and columns
5Cramer's Rule - 3 Variables
Equation speed tips board explaining D first and non-zero D
6Speed Tips

Level Visual Guides

30 levels. Each level opens as 6 visual blocks.

Level 1 visual plan for x + b = c (warm-up)

Level 1 - foundation

x + b = c (warm-up)

6 image blocks

Level 2 visual plan for ax + b = c (small)

Level 2 - foundation

ax + b = c (small)

6 image blocks

Level 3 visual plan for ax + b = c (signed)

Level 3 - realistic untimed

ax + b = c (signed)

6 image blocks

Level 4 visual plan for ax + b = c (mastery)

Level 4 - foundation

ax + b = c (mastery)

6 image blocks

Level 5 visual plan for ax + b = cx + d (small)

Level 5 - foundation

ax + b = cx + d (small)

6 image blocks

Level 6 visual plan for ax + b = cx + d (medium)

Level 6 - foundation

ax + b = cx + d (medium)

6 image blocks

Level 7 visual plan for ax + b = cx + d (signed)

Level 7 - foundation

ax + b = cx + d (signed)

6 image blocks

Level 8 visual plan for ax + b = cx + d (mastery)

Level 8 - realistic untimed

ax + b = cx + d (mastery)

6 image blocks

Level 9 visual plan for 2-var Cramer - find x (small)

Level 9 - foundation

2-var Cramer - find x (small)

6 image blocks

Level 10 visual plan for 2-var Cramer - find y (small)

Level 10 - foundation

2-var Cramer - find y (small)

6 image blocks

Level 11 visual plan for 2-var Cramer - find x (medium)

Level 11 - build-up

2-var Cramer - find x (medium)

6 image blocks

Level 12 visual plan for 2-var Cramer - find y (medium)

Level 12 - build-up

2-var Cramer - find y (medium)

6 image blocks

Level 13 visual plan for 2-var Cramer - find x (signed)

Level 13 - realistic untimed

2-var Cramer - find x (signed)

6 image blocks

Level 14 visual plan for 2-var Cramer - find y (signed)

Level 14 - build-up

2-var Cramer - find y (signed)

6 image blocks

Level 15 visual plan for 2-var Cramer - find x (mastery)

Level 15 - build-up

2-var Cramer - find x (mastery)

6 image blocks

Level 16 visual plan for 2-var Cramer - find y (mastery)

Level 16 - build-up

2-var Cramer - find y (mastery)

6 image blocks

Level 17 visual plan for 3-var Cramer - find x (small)

Level 17 - build-up

3-var Cramer - find x (small)

6 image blocks

Level 18 visual plan for 3-var Cramer - find y (small)

Level 18 - realistic untimed

3-var Cramer - find y (small)

6 image blocks

Level 19 visual plan for 3-var Cramer - find z (small)

Level 19 - build-up

3-var Cramer - find z (small)

6 image blocks

Level 20 visual plan for 3-var Cramer - find x (medium)

Level 20 - build-up

3-var Cramer - find x (medium)

6 image blocks

Level 21 visual plan for 3-var Cramer - find y (medium)

Level 21 - mastery

3-var Cramer - find y (medium)

6 image blocks

Level 22 visual plan for 3-var Cramer - find z (medium)

Level 22 - mastery

3-var Cramer - find z (medium)

6 image blocks

Level 23 visual plan for 3-var Cramer - find x (mastery)

Level 23 - realistic untimed

3-var Cramer - find x (mastery)

6 image blocks

Level 24 visual plan for 3-var Cramer - find y (mastery)

Level 24 - mastery

3-var Cramer - find y (mastery)

6 image blocks

Level 25 visual plan for 3-var Cramer - find z (mastery)

Level 25 - mastery

3-var Cramer - find z (mastery)

6 image blocks

Level 26 visual plan for 2-var realistic - find x (no timer)

Level 26 - realistic untimed

2-var realistic - find x (no timer)

6 image blocks

Level 27 visual plan for 2-var realistic - find y (no timer)

Level 27 - realistic untimed

2-var realistic - find y (no timer)

6 image blocks

Level 28 visual plan for 3-var realistic - find x (no timer)

Level 28 - realistic untimed

3-var realistic - find x (no timer)

6 image blocks

Level 29 visual plan for 3-var realistic - find y (no timer)

Level 29 - realistic untimed

3-var realistic - find y (no timer)

6 image blocks

Level 30 visual plan for 3-var realistic - find z (no timer)

Level 30 - realistic untimed

3-var realistic - find z (no timer)

6 image blocks

Practice this category

Use the same method on live equations & systems levels.

Start Equations & Systems Workout

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