Easy Simultaneous Equations 2

Cards · 52

x + y = 10 and x - y = 2

Add both equations: 2x = 12, so x = 6. Substitute into first: 6 + y = 10, giving y = 4. Solution: (6, 4).

x + y = 7 and x - y = 3

Add equations: 2x = 10, so x = 5. Substitute into x + y = 7: 5 + y = 7, so y = 2. Solution: (5, 2).

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

Add equations: 3x = 9, so x = 3. Substitute into second equation: 3 - y = 1, so y = 2. Solution: (3, 2).

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

Add equations: 2x = 14, so x = 7. Substitute into first: 7 + 2y = 11, giving 2y = 4, so y = 2. Solution: (7, 2).

3x + y = 13 and x + y = 5

Subtract second from first: 2x = 8, so x = 4. Substitute into second: 4 + y = 5, giving y = 1. Solution: (4, 1).

x + y = 9 and 2x - y = 6

Add equations: 3x = 15, so x = 5. Substitute into first: 5 + y = 9, giving y = 4. Solution: (5, 4).

2x + 3y = 12 and 2x + y = 8

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

x - y = 4 and 3x + y = 16

Add equations: 4x = 20, so x = 5. Substitute into first: 5 - y = 4, giving y = 1. Solution: (5, 1).

x + 3y = 10 and x + y = 6

Subtract second from first: 2y = 4, so y = 2. Substitute into second: x + 2 = 6, giving x = 4. Solution: (4, 2).

y = 2x and x + y = 9

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

y = x + 3 and 2x + y = 12

Substitute y into second: 2x + (x + 3) = 12, so 3x = 9, giving x = 3. Then y = 3 + 3 = 6. Solution: (3, 6).

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

Substitute x into second: 3(y - 2) + 2y = 19, so 5y - 6 = 19, 5y = 25, y = 5. Then x = 5 - 2 = 3. Solution: (3, 5).

4x + y = 14 and 2x - y = 4

Add equations: 6x = 18, so x = 3. Substitute into first: 4(3) + y = 14, giving y = 2. Solution: (3, 2).

x + 4y = 14 and x + y = 5

Subtract second from first: 3y = 9, so y = 3. Substitute into second: x + 3 = 5, giving x = 2. Solution: (2, 3).

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

Add equations: 3x = 9, so x = 3. Substitute into second: 3 + y = 4, giving y = 1. Solution: (3, 1).

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

Add equations: 2x = 6, so x = 3. Substitute into second: 3 + 2y = 7, giving 2y = 4, y = 2. Solution: (3, 2).

3x + 2y = 16 and 3x - y = 7

Subtract second from first: 3y = 9, so y = 3. Substitute into second: 3x - 3 = 7, 3x = 10, wait: 3x = 10 gives x = 10/3.

3x + 2y = 16 and x - 2y = 0

Add equations: 4x = 16, so x = 4. Substitute into second: 4 - 2y = 0, giving 2y = 4, y = 2. Solution: (4, 2).

2x + y = 7 and x - 2y = -4

From first, y = 7 - 2x. Substitute into second: x - 2(7 - 2x) = -4, 5x - 14 = -4, 5x = 10, x = 2. Then y = 3. Solution: (2, 3).

x + y = 12 and x - y = 4

Add equations: 2x = 16, so x = 8. Substitute into first: 8 + y = 12, giving y = 4. Solution: (8, 4).

2x + 2y = 10 and 2x - 2y = 2

Add equations: 4x = 12, so x = 3. Substitute into first: 2(3) + 2y = 10, 2y = 4, y = 2. Solution: (3, 2).

5x + y = 16 and 2x - y = 5

Add equations: 7x = 21, so x = 3. Substitute into second: 2(3) - y = 5, giving 6 - y = 5, y = 1. Solution: (3, 1).

x + 2y = 8 and 3x - 2y = 8

Add equations: 4x = 16, so x = 4. Substitute into first: 4 + 2y = 8, 2y = 4, y = 2. Solution: (4, 2).

y = 3x - 1 and 2x + y = 14

Substitute y: 2x + (3x - 1) = 14, so 5x = 15, x = 3. Then y = 3(3) - 1 = 8. Solution: (3, 8).

x = 4y and 2x - 3y = 10

Substitute x: 2(4y) - 3y = 10, 8y - 3y = 10, 5y = 10, y = 2. Then x = 4(2) = 8. Solution: (8, 2).

2x + 3y = 13 and x + 3y = 11

Subtract second from first: x = 2. Substitute into second: 2 + 3y = 11, giving 3y = 9, so y = 3. Solution: (2, 3).

4x - y = 9 and 2x + y = 9

Add equations: 6x = 18, so x = 3. Substitute into second: 2(3) + y = 9, giving 6 + y = 9, y = 3. Solution: (3, 3).

x + y = 15 and x - y = 5

Add equations: 2x = 20, so x = 10. Substitute into first: 10 + y = 15, giving y = 5. Solution: (10, 5).

3x + y = 11 and x - y = 1

Add equations: 4x = 12, so x = 3. Substitute into second: 3 - y = 1, giving y = 2. Solution: (3, 2).

x - 3y = -7 and x + 3y = 11

Add equations: 2x = 4, so x = 2. Substitute into second: 2 + 3y = 11, giving 3y = 9, y = 3. Solution: (2, 3).

2x + y = 9 and 3x - y = 6

Add equations: 5x = 15, so x = 3. Substitute into first: 2(3) + y = 9, 6 + y = 9, y = 3. Solution: (3, 3).

x + 2y = 9 and x - y = 3

Subtract second from first: 3y = 6, so y = 2. Substitute into second: x - 2 = 3, giving x = 5. Solution: (5, 2).

y = 4 - x and 3x + y = 8

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

x + y = 1 and 2x + y = 4

Subtract first from second: x = 3. Substitute into first: 3 + y = 1, giving y = -2. Solution: (3, -2).

2x + y = 11 and x + y = 7

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

5x - 2y = 8 and 3x + 2y = 8

Add equations: 8x = 16, so x = 2. Substitute into second: 3(2) + 2y = 8, 6 + 2y = 8, y = 1. Solution: (2, 1).

x - 4y = -2 and x + 2y = 10

Subtract first from second: 6y = 12, so y = 2. Substitute into second: x + 2(2) = 10, giving x = 6. Solution: (6, 2).

3x - y = 5 and 2x + y = 10

Add equations: 5x = 15, so x = 3. Substitute into second: 2(3) + y = 10, 6 + y = 10, y = 4. Solution: (3, 4).

x + 5y = 13 and x + 2y = 7

Subtract second from first: 3y = 6, so y = 2. Substitute into second: x + 2(2) = 7, giving x = 3. Solution: (3, 2).

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

Substitute y: 2x + 3(x - 4) = 13, 5x - 12 = 13, 5x = 25, x = 5. Then y = 5 - 4 = 1. Solution: (5, 1).

x + y = 8 and 3x - y = 4

Add equations: 4x = 12, so x = 3. Substitute into first: 3 + y = 8, giving y = 5. Solution: (3, 5).

4x + 3y = 17 and x + 3y = 11

Subtract second from first: 3x = 6, so x = 2. Substitute into second: 2 + 3y = 11, 3y = 9, y = 3. Solution: (2, 3).

2x - 3y = -1 and x + 3y = 10

Add equations: 3x = 9, so x = 3. Substitute into second: 3 + 3y = 10, wait: 3y = 7 gives y = 7/3.

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

Add equations: 3x = 6, so x = 2. Substitute into second: 2 + 3y = 7, giving 3y = 5, y = 5/3.

x + y = 6 and 2x - y = 0

Add equations: 3x = 6, so x = 2. Substitute into first: 2 + y = 6, giving y = 4. Solution: (2, 4).

3x + 2y = 12 and x - y = -1

From second, x = y - 1. Substitute into first: 3(y - 1) + 2y = 12, 5y - 3 = 12, 5y = 15, y = 3. Then x = 2. Solution: (2, 3).

x + 2y = 10 and 3x + y = 15

From first, x = 10 - 2y. Substitute: 3(10 - 2y) + y = 15, 30 - 5y = 15, 5y = 15, y = 3. Then x = 4. Solution: (4, 3).

2x + y = 10 and 2x - y = 2

Add equations: 4x = 12, so x = 3. Substitute into first: 2(3) + y = 10, giving y = 4. Solution: (3, 4).

x - y = -2 and x + 2y = 7

Subtract first from second: 3y = 9, so y = 3. Substitute into first: x - 3 = -2, giving x = 1. Solution: (1, 3).

3x + 4y = 18 and x - y = -1

From second, x = y - 1. Substitute: 3(y - 1) + 4y = 18, 7y - 3 = 18, 7y = 21, y = 3. Then x = 2. Solution: (2, 3).

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

From first, x = 7 - 3y. Substitute: 2(7 - 3y) - y = 7, 14 - 7y = 7, 7y = 7, y = 1. Then x = 4. Solution: (4, 1).

2x + 5y = 19 and 2x + y = 7

Subtract second from first: 4y = 12, so y = 3. Substitute into second: 2x + 3 = 7, 2x = 4, x = 2. Solution: (2, 3).