Answer:
11. (x, y) -> (7, -3)
14. (x, y) -> (-3, -2)
15. (x, y) -> (-3, 2)
16. (x, y) -> (7,6)
20.(x, y) -> (4, 1)
Step-by-step explanation:
11.
x + 3y = 1
-3x -3y = -15
-2x = -14
/-2 /-2
x = 7
x + 3y = 1
7 + 3y = 1
-7 -7
3y = -6
/3 /3
y = -2
(x, y) -> (7, -3)
14.
-3x + 3y = 3
-5x + y = 13
-5x + y = 13
+5x +5x
y = 5x + 13
-3x + 3(5x + 13) = 3
-3x + 15x + 39 = 3
12x + 39 = 3
- 39 -39
12x = -36
/12 /12
x = -3
Now, we solve for y:
-5x + y = 13
-5(-3) + y = 13
15 + y = 13
-15 -15
y = -2
(x, y) -> (-3, -2)
15.
6x + 6y = -6
5x + y = -13
5x + y = -13
-5x -5x
y = -5x - 13
6x + 6y = -6
6x + 6(-5x - 13) = -6
6x -30x - 78 = -6
-24x - 78 = -6
+ 78 + 78
-24x = 72
/-24 /-24
x = -3
Now, we solve for y:
6x + 6y = -6
6x + 6y = -6
6(-3) + 6y = -6
-18 + 6y = -6
+18 +18
6y = 12
/6 /6
y = 2
(x, y) -> (-3, 2)
16.
2x + y = 20
6x - 5y = 12
2x + y = 20
-2x -2x
y = -2x + 20
6x - 5y = 12
6x - 5(-2x + 20) = 12
6x + 10x - 100 = 12
16x - 100 = 12
+ 100 +100
16x = 112
/16 /16
x = 7
Now, we solve for y:
2x + y = 20
2(7) + y = 20
14 + y = 20
-14 -14
y = 6
(x, y) -> (7,6)
20.
-2x - y = -9
5x - 2y = 18
-2x - y = -9
+2x +2x
-y = 2x - 9
/-1 /-1
y = -2x + 9
5x -2y = 18
5x - 2(-2x + 9) = 18
5x + 4x - 18 = 18
9x - 18 = 18
+ 18 + 18
9x = 36
/9 /9
x = 4
Now, we solve for y:
-2(4) - y = -9
-8 - y = -9
+ 8 +8
-y = -1
/-1 /-1
y = 1
(x, y) -> (4, 1)
Hope this helps!
