Easy Simultaneous Equations

Cards · 53

x + y = 6, x - y = 2

Add equations: 2x = 8 -> x = 4. Substitute into first equation: 4 + y = 6 -> y = 2. Solution: (4, 2).

x + y = 10, x - y = 4

Add equations: 2x = 14 -> x = 7. Substitute into first equation: 7 + y = 10 -> y = 3. Solution: (7, 3).

x + y = 8, x - y = 6

Add equations: 2x = 14 -> x = 7. Substitute: 7 + y = 8 -> y = 1. Solution: (7, 1).

x + y = 12, x - y = 0

Add equations: 2x = 12 -> x = 6. Substitute: 6 + y = 12 -> y = 6. Solution: (6, 6).

x + y = 5, x - y = 3

Add equations: 2x = 8 -> x = 4. Substitute: 4 + y = 5 -> y = 1. Solution: (4, 1).

x + y = 7, x - y = 1

Add equations: 2x = 8 -> x = 4. Substitute: 4 + y = 7 -> y = 3. Solution: (4, 3).

x + y = 9, x - y = 5

Add equations: 2x = 14 -> x = 7. Substitute: 7 + y = 9 -> y = 2. Solution: (7, 2).

x + y = 15, x - y = 5

Add equations: 2x = 20 -> x = 10. Substitute: 10 + y = 15 -> y = 5. Solution: (10, 5).

x + y = 3, x - y = -1

Add equations: 2x = 2 -> x = 1. Substitute: 1 + y = 3 -> y = 2. Solution: (1, 2).

x + y = 2, x - y = 4

Add equations: 2x = 6 -> x = 3. Substitute: 3 + y = 2 -> y = -1. Solution: (3, -1).

x + 2y = 8, x + y = 5

Subtract second from first: y = 3. Substitute into second: x + 3 = 5 -> x = 2. Solution: (2, 3).

x + 2y = 11, x + y = 7

Subtract second from first: y = 4. Substitute: x + 4 = 7 -> x = 3. Solution: (3, 4).

x + 3y = 10, x + y = 4

Subtract second from first: 2y = 6 -> y = 3. Substitute: x + 3 = 4 -> x = 1. Solution: (1, 3).

2x + y = 7, x + y = 4

Subtract second from first: x = 3. Substitute: 3 + y = 4 -> y = 1. Solution: (3, 1).

3x + y = 11, x + y = 5

Subtract second from first: 2x = 6 -> x = 3. Substitute: 3 + y = 5 -> y = 2. Solution: (3, 2).

2x + y = 9, x - y = 0

From second, y = x. Substitute into first: 2x + x = 9 -> 3x = 9 -> x = 3. Thus, y = 3. Solution: (3, 3).

x - 2y = 1, x + y = 7

Subtract first from second: 3y = 6 -> y = 2. Substitute: x + 2 = 7 -> x = 5. Solution: (5, 2).

y = 2x, x + y = 9

Substitute y = 2x into second: x + 2x = 9 -> 3x = 9 -> x = 3. Then y = 2(3) = 6. Solution: (3, 6).

y = 3x, 2x + y = 15

Substitute y = 3x into second: 2x + 3x = 15 -> 5x = 15 -> x = 3. Then y = 3(3) = 9. Solution: (3, 9).

x = 4y, x - y = 6

Substitute x = 4y into second: 4y - y = 6 -> 3y = 6 -> y = 2. Then x = 4(2) = 8. Solution: (8, 2).

y = x + 2, 2x + y = 8

Substitute y: 2x + (x + 2) = 8 -> 3x = 6 -> x = 2. Then y = 2 + 2 = 4. Solution: (2, 4).

y = 2x - 1, 3x - y = 4

Substitute y: 3x - (2x - 1) = 4 -> x + 1 = 4 -> x = 3. Then y = 2(3) - 1 = 5. Solution: (3, 5).

x = y + 3, 2x + 3y = 16

Substitute x: 2(y + 3) + 3y = 16 -> 5y + 6 = 16 -> 5y = 10 -> y = 2. Then x = 2 + 3 = 5. Solution: (5, 2).

2x + 3y = 8, x + 3y = 7

Subtract second from first: x = 1. Substitute: 1 + 3y = 7 -> 3y = 6 -> y = 2. Solution: (1, 2).

3x + 2y = 12, 3x + y = 9

Subtract second from first: y = 3. Substitute: 3x + 3 = 9 -> 3x = 6 -> x = 2. Solution: (2, 3).

2x - y = 4, x + y = 5

Add equations: 3x = 9 -> x = 3. Substitute: 3 + y = 5 -> y = 2. Solution: (3, 2).

3x - y = 7, 2x + y = 8

Add equations: 5x = 15 -> x = 3. Substitute: 2(3) + y = 8 -> 6 + y = 8 -> y = 2. Solution: (3, 2).

4x + y = 13, 2x - y = 5

Add equations: 6x = 18 -> x = 3. Substitute: 4(3) + y = 13 -> 12 + y = 13 -> y = 1. Solution: (3, 1).

2x + 3y = 13, x - 2y = -4

From second, x = 2y - 4. Substitute: 2(2y - 4) + 3y = 13 -> 7y - 8 = 13 -> 7y = 21 -> y = 3. x = 2(3) - 4 = 2. Solution: (2, 3).

2x + y = 10, 3x - 2y = 8

Multiply first by 2: 4x + 2y = 20. Add to second: 7x = 28 -> x = 4. Substitute: 2(4) + y = 10 -> y = 2. Solution: (4, 2).

3x + 2y = 13, x + 4y = 11

Multiply second by 3: 3x + 12y = 33. Subtract first: 10y = 20 -> y = 2. Substitute: x + 4(2) = 11 -> x = 3. Solution: (3, 2).

2x + 5y = 16, 2x + y = 8

Subtract second from first: 4y = 8 -> y = 2. Substitute: 2x + 2 = 8 -> 2x = 6 -> x = 3. Solution: (3, 2).

3x + 4y = 18, x + 2y = 8

Multiply second by 2: 2x + 4y = 16. Subtract from first: x = 2. Substitute: 2 + 2y = 8 -> 2y = 6 -> y = 3. Solution: (2, 3).

4x + 3y = 18, 2x + y = 8

Multiply second by 2: 4x + 2y = 16. Subtract from first: y = 2. Substitute: 2x + 2 = 8 -> 2x = 6 -> x = 3. Solution: (3, 2).

5x - y = 9, 2x + y = 5

Add equations: 7x = 14 -> x = 2. Substitute: 2(2) + y = 5 -> 4 + y = 5 -> y = 1. Solution: (2, 1).

x + 4y = 14, 3x - 2y = 0

From second, 3x = 2y -> y = 1.5x. Substitute: x + 6x = 14 -> 7x = 14 -> x = 2. Then y = 3. Solution: (2, 3).

2x - 3y = -1, x + y = 7

From second, x = 7 - y. Substitute: 2(7 - y) - 3y = -1 -> 14 - 5y = -1 -> 5y = 15 -> y = 3. Then x = 7 - 3 = 4. Solution: (4, 3).

4x - y = 7, 2x + 3y = 21

From first, y = 4x - 7. Substitute: 2x + 3(4x - 7) = 21 -> 14x - 21 = 21 -> 14x = 42 -> x = 3. y = 4(3) - 7 = 5. Solution: (3, 5).

3x + 2y = 7, 2x - y = 7

Multiply second by 2: 4x - 2y = 14. Add to first: 7x = 21 -> x = 3. Substitute: 2(3) - y = 7 -> 6 - y = 7 -> y = -1. Solution: (3, -1).

x + 2y = 0, 3x + 4y = -4

From first, x = -2y. Substitute: 3(-2y) + 4y = -4 -> -2y = -4 -> y = 2. Then x = -2(2) = -4. Solution: (-4, 2).

2x + 3y = 12, 3x + 2y = 13

Add equations: 5x + 5y = 25 -> x + y = 5. Subtract equations: -x + y = -1. Add these two: 2y = 4 -> y = 2, so x = 3. Solution: (3, 2).

3x + 5y = 11, 2x - y = 3

Multiply second by 5: 10x - 5y = 15. Add to first: 13x = 26 -> x = 2. Substitute: 2(2) - y = 3 -> 4 - y = 3 -> y = 1. Solution: (2, 1).

x - 3y = 2, 2x + y = 11

Multiply second by 3: 6x + 3y = 33. Add to first: 7x = 35 -> x = 5. Substitute: 2(5) + y = 11 -> 10 + y = 11 -> y = 1. Solution: (5, 1).

5x + 2y = 16, 3x + y = 9

Multiply second by 2: 6x + 2y = 18. Subtract first: x = 2. Substitute: 3(2) + y = 9 -> 6 + y = 9 -> y = 3. Solution: (2, 3).

2x + 4y = 10, x + y = 3

Multiply second by 2: 2x + 2y = 6. Subtract from first: 2y = 4 -> y = 2. Substitute: x + 2 = 3 -> x = 1. Solution: (1, 2).

3x - 2y = 12, x + 2y = 4

Add equations: 4x = 16 -> x = 4. Substitute: 4 + 2y = 4 -> 2y = 0 -> y = 0. Solution: (4, 0).

2x + y = 1, x - 2y = 8

Multiply first by 2: 4x + 2y = 2. Add to second: 5x = 10 -> x = 2. Substitute: 2(2) + y = 1 -> 4 + y = 1 -> y = -3. Solution: (2, -3).

4x + 2y = 14, 3x - y = 8

Multiply second by 2: 6x - 2y = 16. Add to first: 10x = 30 -> x = 3. Substitute: 3(3) - y = 8 -> 9 - y = 8 -> y = 1. Solution: (3, 1).

x + 5y = 11, 2x - y = 0

From second, y = 2x. Substitute into first: x + 5(2x) = 11 -> 11x = 11 -> x = 1. Then y = 2(1) = 2. Solution: (1, 2).

2x - 3y = 7, x + y = 1

Multiply second by 3: 3x + 3y = 3. Add to first: 5x = 10 -> x = 2. Substitute: 2 + y = 1 -> y = -1. Solution: (2, -1).

3x + 4y = 10, 2x - 4y = 0

Add equations: 5x = 10 -> x = 2. Substitute: 2(2) - 4y = 0 -> 4 - 4y = 0 -> y = 1. Solution: (2, 1).

x + 3y = 6, 2x - y = 5

Multiply second by 3: 6x - 3y = 15. Add to first: 7x = 21 -> x = 3. Substitute: 3 + 3y = 6 -> 3y = 3 -> y = 1. Solution: (3, 1).

2x + 3y = 19, x - y = 2

From second, x = y + 2. Substitute: 2(y + 2) + 3y = 19 -> 5y + 4 = 19 -> 5y = 15 -> y = 3. Then x = 3 + 2 = 5. Solution: (5, 3).