<h3>1) <u>What is the solution for the system of equations</u></h3>
-2x+y=2...(i)
y=4x-1...(ii)
substitute y in (i)
-2x+(4x-1)=2
-2x+4x-1=2
-2x+4x=2+1
2x=3
2x/2=3/2
x=3/2
replacing x in (ii)
y=4(3/2)-1
y=6-1
y=5
solution=(3/2,5)
<h3 /><h3>2) <u>Solve the system of equations.</u></h3>
x-y+z=6 ...(i)
4y+1=z ...(ii)
3y=2z...(iii)
from(ii),
z=4y+1
substitute z in (iii)
3y=2(4y+1)
3y=8y+2
3y-8y=2
-5y=2
-5y/5=2/5
y=-2/5
substitute y in (ii)
z=4(-2/5)+1
z=-3/5
substitute z and y in (i)
x-y+z=6
x=6+y-z
x=6+(-2/5)-(-3/5)
x=31/5
solution=(31/5,-2/5,-3/5)
<h3>
3) <u>What is the solution for the system of equations</u></h3>
-4x+y=-2 ...(i)
y+5=-6x...(ii)
from (i),
y=-2+4x
substitute y in (ii)
(-2+4x)+5=-6x
-2+4x+5=-6x
-2+5=-6x-4x
3=-10x
3/-10=-10x/-10
x=-3/10
substitute x in;;y=-2+4x
y=-2+4(-3/10)
y=-2-6/5
y=-16/5
solution=(-3/10,-16/5)
The area of parallelogram is 108 square inches
<em><u>Solution:</u></em>
<em><u>The formula for area of parallelogram is:</u></em>
![Area = base \times height](https://tex.z-dn.net/?f=Area%20%3D%20base%20%5Ctimes%20height)
From given,
![Base = 1\frac{1}{2}\ feet = \frac{2 \times 1 + 1}{2} = \frac{3}{2}\ feet](https://tex.z-dn.net/?f=Base%20%3D%201%5Cfrac%7B1%7D%7B2%7D%5C%20feet%20%3D%20%5Cfrac%7B2%20%5Ctimes%201%20%2B%201%7D%7B2%7D%20%3D%20%5Cfrac%7B3%7D%7B2%7D%5C%20feet)
![Height = 6\ inches](https://tex.z-dn.net/?f=Height%20%3D%206%5C%20inches)
<em><u>Convert feet to inches</u></em>
1 feet = 12 inches
![\frac{3}{2}\ feet = \frac{3}{2} \times 12\ inches = 18\ inches](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B2%7D%5C%20feet%20%3D%20%5Cfrac%7B3%7D%7B2%7D%20%5Ctimes%2012%5C%20inches%20%3D%2018%5C%20inches)
<em><u>Therefore, area of parallelogram is:</u></em>
![Area = 18 \times 6\\\\Area = 108](https://tex.z-dn.net/?f=Area%20%3D%2018%20%5Ctimes%206%5C%5C%5C%5CArea%20%3D%20108)
Thus area of parallelogram is 108 square inches
Answer:
17 students
Step-by-step explanation:
the bus will take all the students so
932.50 - 550 = 382.5
and a meal for each student so
382.5 ÷ 22.5 = 17