Equations with two unknowns

Mathematics · Algebra · ages 10-11

Name ______________________ Date ____________

If a + b = 12 and a = 5, what is b?
Answer: ______________
Which whole-number pair satisfies a + b = 12?
- (5, 7)
- (5, 6)
- (4, 7)
- (7, 7)
Which pair of whole numbers fits a + b = 10?
- 4 and 6
- 4 and 5
- 4 and 7
For 2x + y = 20, which pair fits the rule?
- x = 5, y = 15
- x = 5, y = 10
- x = 5, y = 5
For 2x + y = 20, if x = 8, what is y?
- 12
- 4
- 16
The rules say a and b must be above 0 in a + b = 12, so (12, 0) is banned. Is that correct?
Circle one: True False
Which pair satisfies 2x + y = 20?
- (6, 6)
- (8, 6)
- (6, 8)
- (5, 8)
For a + b = 12, if a = 5, what must b be?
Answer: ______________
Ravi lists pairs for a + b = 8: (1,7), (2,6), (3,5), (4,4). He says that is every possible pair of whole numbers greater than 0. Is he right?
- Yes, he found every pair
- No, he should also include (0,8) and (8,0)
- No, he is missing (5,3), (6,2), and (7,1)
How many whole-number pairs (a, b) with a and b above 0 satisfy a + b = 12?
- 12
- 10
- 13
- 11

Answer key

For grown-ups. Fold this page away before handing over the rest.

7 · b = 12 - 5 = 7.
(5, 7) · 5 + 7 = 12. The rest give 11 or 14.
4 and 6 · 4 + 6 = 10, so this pair fits the rule. The other pairs add up to 9 or 11, not 10.
x = 5, y = 10 · 2 times 5 is 10, and 10 + 10 = 20, so this pair works. The other pairs do not add up to 20.
4 · 2 times 8 is 16. Then 20 - 16 leaves 4, so y = 4.
True · It is correct: both must be above 0, and 0 fails that.
(6, 8) · 2 x 6 + 8 = 20.
7 · 12 - 5 = 7, so b must be 7 to make the equation true.
No, he is missing (5,3), (6,2), and (7,1) · Once a passes 4, new pairs appear by swapping the numbers: (5,3), (6,2), and (7,1) also add to 8.
11 · a can be 1 through 11, giving 11 pairs.