Answer:
20. x = 5, y = -2
21. x = 11, y = 12
22. x = 22, y = 11
23. x = 11, y = 10
Step-by-step explanation:
20. Opposite sides in the parallelogram are congruent, so
![2y+18=3x-1\\ \\6x-3=17-5y](https://tex.z-dn.net/?f=2y%2B18%3D3x-1%5C%5C%20%5C%5C6x-3%3D17-5y)
Solve this system of two equations:
![\left\{\begin{array}{l}2y-3x=-19\\ \\6x+5y=20\end{array}\right.](https://tex.z-dn.net/?f=%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bl%7D2y-3x%3D-19%5C%5C%20%5C%5C6x%2B5y%3D20%5Cend%7Barray%7D%5Cright.)
Multiply the first equation by 2 and add two equations:
![2(2y-3x)+6x+5y=2\cdot (-19)+20\\ \\4y-6x+6x+5y=-38+20\\ \\9y=-18\\ \\y=-2](https://tex.z-dn.net/?f=2%282y-3x%29%2B6x%2B5y%3D2%5Ccdot%20%28-19%29%2B20%5C%5C%20%5C%5C4y-6x%2B6x%2B5y%3D-38%2B20%5C%5C%20%5C%5C9y%3D-18%5C%5C%20%5C%5Cy%3D-2)
Substitute it into the first equation:
![2\cdot (-2)-3x=-19\\ \\-3x=-19+4\\ \\-3x=-15\\ \\x=5](https://tex.z-dn.net/?f=2%5Ccdot%20%28-2%29-3x%3D-19%5C%5C%20%5C%5C-3x%3D-19%2B4%5C%5C%20%5C%5C-3x%3D-15%5C%5C%20%5C%5Cx%3D5)
21. Opposite angles in the parallelogram are congruent, so
![11x+5=10y+6](https://tex.z-dn.net/?f=11x%2B5%3D10y%2B6)
Consecutive angles are supplementary, so
![6x-y+11x+5=180^{\circ}](https://tex.z-dn.net/?f=6x-y%2B11x%2B5%3D180%5E%7B%5Ccirc%7D)
Solve this system of two equations:
![\left\{\begin{array}{l}11x-10y=1\\ \\17x-y=175\end{array}\right.](https://tex.z-dn.net/?f=%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bl%7D11x-10y%3D1%5C%5C%20%5C%5C17x-y%3D175%5Cend%7Barray%7D%5Cright.)
From the second equation
![y=17x-175](https://tex.z-dn.net/?f=y%3D17x-175)
Substitute it into the first equation:
![11x-10(17x-175)=1\\ \\11x-170x+1750=1\\ \\-159x=-1749\\ \\x=11\\ \\y=17\cdot 11-175=187-175=12](https://tex.z-dn.net/?f=11x-10%2817x-175%29%3D1%5C%5C%20%5C%5C11x-170x%2B1750%3D1%5C%5C%20%5C%5C-159x%3D-1749%5C%5C%20%5C%5Cx%3D11%5C%5C%20%5C%5Cy%3D17%5Ccdot%2011-175%3D187-175%3D12)
22. Opposite angles in the parallelogram are congruent, so
![2x-5=3y-12](https://tex.z-dn.net/?f=2x-5%3D3y-12)
Consecutive angles are supplementary, so
![2x-5+7y+x=180^{\circ}](https://tex.z-dn.net/?f=2x-5%2B7y%2Bx%3D180%5E%7B%5Ccirc%7D)
Solve this system of two equations:
![\left\{\begin{array}{l}2x-3y=-7\\ \\3x+7y=185\end{array}\right.](https://tex.z-dn.net/?f=%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bl%7D2x-3y%3D-7%5C%5C%20%5C%5C3x%2B7y%3D185%5Cend%7Barray%7D%5Cright.)
From the first equation
![x=-3.5+1.5y](https://tex.z-dn.net/?f=x%3D-3.5%2B1.5y)
Substitute it into the second equation:
![3(-3.5+1.5y)+7y=185\\ \\-10.5+4.5y+7y=185\\ \\-105+45y+70y=1,850\\ \\115y=1,850+105\\ \\115y=1,955\\ \\y=17\\ \\x=-3.5+1.5\cdot 17=22](https://tex.z-dn.net/?f=3%28-3.5%2B1.5y%29%2B7y%3D185%5C%5C%20%5C%5C-10.5%2B4.5y%2B7y%3D185%5C%5C%20%5C%5C-105%2B45y%2B70y%3D1%2C850%5C%5C%20%5C%5C115y%3D1%2C850%2B105%5C%5C%20%5C%5C115y%3D1%2C955%5C%5C%20%5C%5Cy%3D17%5C%5C%20%5C%5Cx%3D-3.5%2B1.5%5Ccdot%2017%3D22)
23. Opposite sides in the parallelogram are congruent, so
![2x+9=4y-9\\ \\3x-5=2y+8](https://tex.z-dn.net/?f=2x%2B9%3D4y-9%5C%5C%20%5C%5C3x-5%3D2y%2B8)
Solve this system of two equations:
![\left\{\begin{array}{l}2x-4y=-18\\ \\3x-2y=13\end{array}\right.](https://tex.z-dn.net/?f=%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bl%7D2x-4y%3D-18%5C%5C%20%5C%5C3x-2y%3D13%5Cend%7Barray%7D%5Cright.)
Multiply the second equation by 2 and subtract it from the first equation:
![2x-4y-2(3x-2y)=-18-2\cdot 13\\ \\2x-4y-6x+4y=-18-26\\ \\-4x=-44\\ \\x=11](https://tex.z-dn.net/?f=2x-4y-2%283x-2y%29%3D-18-2%5Ccdot%2013%5C%5C%20%5C%5C2x-4y-6x%2B4y%3D-18-26%5C%5C%20%5C%5C-4x%3D-44%5C%5C%20%5C%5Cx%3D11)
Substitute it into the first equation:
![2\cdot 11-4y=-18\\ \\-4y=-18-22\\ \\-4y=-40\\ \\y=10](https://tex.z-dn.net/?f=2%5Ccdot%2011-4y%3D-18%5C%5C%20%5C%5C-4y%3D-18-22%5C%5C%20%5C%5C-4y%3D-40%5C%5C%20%5C%5Cy%3D10)