- Published: September 13, 2022
- Updated: September 13, 2022
- University / College: University of Tasmania
- Language: English
- Downloads: 22
Select any two integers between -12 and 12 which will become solutions to a system of two equations.
(1, 1/2) or x= 1 and y= 1/2
Write two equations that have your two integers as solutions.
2x+2y= 3 First Equation
2x+2y = 1 Second Equation
Show how you built the equations using your integers.
let x = 1 And y = 1/2
Now 4x + 0= 4
And y= 1/2 therefore 2y= 1
2(1) +2y= 3 thus 2x+2y= 3
Now adding: {2x+2y= 3}+{_x – _y= _}={4x + 0= 4} which yields 2x+2y= 1
Solve the system of equations by the addition/subtraction method.
{2x+2y= 3} + {2x+2y= 1} = 4x + 0= 4
The terms containing y add up to zero and gives
4x + 0= 4 hence x = 1
Now we know x and can solve for y by substituting the now known value for x into either of our original equations.
2x+2y= 3
2(1)+2y= 3; 2y= 3-2 = 1 and so y= 1/2
Question 2:
Dimensions of the room in
the length= 4m= 13. 12ft
the width= 3m= 9. 84ft
the height= 3. 5m= 11. 48ft
Converting the measurements to all inches
the length= 4m= 157. 48in
the width= 3m= 118. 11in
the height= 3. 5m= 137. 8in
converting back to square feet
13. 12ft= 172. 13sq. ft
9. 84ft= 96. 83 sq. ft
11. 48ft= 131. 79 sq. ft
surface area of the room=(L*H +W*H)*2=(13. 12*11. 48 + 9. 84*11. 48)*2= 527. 16 sq. ft
A gallon of paint covers about 350 square feet.
gallons required to paint the room= (527. 16 sq. ft/350 square feet)*1 gallon = 1. 5 gallons
that is 2 gallons.
a gallon of paint costs $22. 95 plus (8/100)*22. 95= $24. 786
the total cost to paint the room= $24. 786 *2 = $49. 572
One inch is equivalent to 2. 54 centimeters. therefore
the length= 4m= 157. 48in*2. 54= 400cm
the width= 3m= 118. 11in*2. 54= 300cm
the height= 3. 5m= 137. 8in*2. 54= 350cm
Find the volume in cubic centimeters.
Volume = L*W*H = 400*300*350 = 42*106 cubic centimeters
If each dimension (length, width, and height) is doubled,
The volume of the room doubles = (400*300*350) = 84*106 cubic centimeters
