Directions: Using the integers -9 to 9 (excluding 0) at most one time each, fill in the blanks to create two distinct perpendicular lines.

### Hint

Why might we want to consider the relationship between the coefficients of x and y?

### Answer

There are many solutions but not infinite

1 x + 2 y = 4

-6 x + 3 y = 5

2 x + 3 y = 9

-6 x + 4 y = 8

Any solution where the x and y coefficients swap and one is negative. Students will need to use multiples to avoid repeating values. The constant term can take any remaining value.

Source: Louise Pepper with answers from the students of Kings College Alicante, Spain

2x+6y=9

-8+4y=8

Anyone else bored with online school?

@Yeet

Yup. Although I am actually going to school… I miss my friends.

I got 2x+6y=9

-8+4y=8

1x +2y =4

3x+-6=5

2x + 6y = 9

-8x + 4y = 8

6x+3y=15

12x+6y=30