Answer:
3. (x, y) = (3, 2)
6. (x, y) = (10, 4/3)
9. (x, y) = (-2, -1)
12. (x, y) = (8, 3)
Explanation:
3, 6. See the attachment. 3 is graphed in red/orange. 6 is graphed in blue, purple.
__
9. Use the expression for y in the second equation to substitute for y in the first equation:
4(3x +5) -x = -2
12x +20 -x = -2 . . . eliminate parentheses
11x = -22 . . . . . . . . subtract 20, collect terms
x = -2 . . . . . . . . . . . divide by 11
y = 3(-2) +5 = -1 . . .substitute for x in the second equation
The solution is (x, y) = (-2, -1).
__
12. Subtract 3/4x from the second equation to get an expression for y:
y = 9 - 3/4x
Substitute that into the first equation:
3(9 -3/4x) -5/4x = -1
27 -9/4x -5/4x = -1 . . . . eliminate parentheses
-14/4x = -28 . . . . . . . . . . collect terms, subtract 27
x = 8 . . . . . . . . . . . . . . . . multiply by -4/14
y = 9 -3/4(8) = 3 . . . . . . substitute into the expression for y
The solution is (x, y) = (8, 3).