-252 + 352 = 100 5. Pattern: For x = 11n -3 For y = 7n - 3 Equations describing solutions: Solution 1: x= 8 y=4 Solution 2: x=33 y=-3 Solution 3: x=30 y=-110 Solution 4: x=-3 y=11 Solution 5: x=-14 y=18 Solution 6: x=-25 y=25 Solution 7: x=-37 y=32 Explanation: For every negative and positive multiples of 7 and 11 I’ve highlighted every solution with the same color. For example I highlighted -21 from multiples of 7 and 121 from multiples of 11 in orange and those two numbers added are a solution for our investigation. I’ve done the same thing for 1. In number 4, I put all the solution in a table but now with the full equation. In 5, I wrote the pattern for X which is x=11n-3 and for Y which is y=7n-3. Below that are the equations more specific.
Investigation 7x +11y = 100
1.
Multiples of 7:
7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, 126, 133, 140
Multiples of 11:
11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143, 154, 165, 176, 187, 198, 209, 220
2.
Values of x and y:
Solution 1
3.
Negative and positive multiples of 7:
-7, -14, -21, -28, -35, -52, -49, -56, -63, -70, -77, -84, -91, -98, -105, -112, -119, -126, -133, -140, -147, -154, -161, -168, -175, -182, -189, -196, -203, -210, -217, -224, -231, -238, -245, -252
7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, 126, 133, 140, 147, 154, 161, 168, 175, 182, 189, 196, 203, 210, 217, 224, 231, 238, 245, 252
Negatives and positive multiples of 11:
-11, -22, -33, -44, -55, -66, -77, -88, -99, -110, -121, -132, -143, -154, -165, -176, -187, -198, -209, -220, -231, -242, -253, -264, -275, -286, -297, -308, -319, -330, -341, -352
11, 22, 33, 4, 55, 66, 77, 88, 99, 110, 121, 132, 143, 154, 165, 176, 187, 198, 209, 220, 231, 242, 253, 264, 275, 286, 297, 308, 319, 330, 341, 352
4.
Solution 2
Solution 3
Solution 4
Solution 5
Solution 6
Solution 7
5.
Pattern:
For x = 11n -3
For y = 7n - 3
Equations describing solutions:
Solution 1: x= 8 y=4
Solution 2: x=33 y=-3
Solution 3: x=30 y=-110
Solution 4: x=-3 y=11
Solution 5: x=-14 y=18
Solution 6: x=-25 y=25
Solution 7: x=-37 y=32
Explanation:
For every negative and positive multiples of 7 and 11 I’ve highlighted every solution with the same color. For example I highlighted -21 from multiples of 7 and 121 from multiples of 11 in orange and those two numbers added are a solution for our investigation.
I’ve done the same thing for 1.
In number 4, I put all the solution in a table but now with the full equation. In 5, I wrote the pattern for X which is x=11n-3 and for Y which is y=7n-3.
Below that are the equations more specific.