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
