HW4 system of Linear Help with Re-checking and help with problem.

Question

For this, I have completed most problems using the elimination problem method, However, could someone check to see if this is right for problem 6? And could I get help on 8 and 9

6.) x + y =3

2x +2y=6

Answer: (No solutions to the problem (0=0)

8.) An herb that sells for $5.00 per pound is mixed with tea that sells for $3.20 per pound to produce a 100-pound mix that is worth $3.66 per pound. How many pounds of each ingredient does the mix contain?

a.) System of eqns requires equations! What two quantities (not products) are identified in the problem?

b.) If those two quantities remain constant during the mixing process, you have two eqns.

c.) Solve and check.

9.) Challenged problem; A chemist had a soln of 60% acid. She added some distilled water, reducing the acid concentrations to 40%. She then added one more liter of water to further reduce the acid concentrations to 30%. How much of the 30% solution did she then have?

a.) Is the original amount soln known?

b.) Is the amount of water added during the first dilutions known?

c.) Does the amount of pure acid change during this process? When things don't change, they remain equal, and that suggests an equation.

d.) Solve and checks

Answer 1

6) infinite solutions

x+y=3

2x+2y=6

y=3-x

x=3-y

solutions= (x,y)

= (x, 3-x) where x = any real number

= (3-y, y) where y = any real number

such as (3,0), (0,3), or (-3,6)

graph x+y=0, it's a straight line with intercepts (3,0) and (0,3) any point on that line is a solution to

the two equations. that's an infinite number of solutions

8) 5x+3.2y =3.66(100)=366

5x +3.2(100-x)=366

1.8x = 366-320= 46

x= 46/1.8= 460/18=230/9= 25 5/9 lbs of herb

y= 74 4/9 lbs of tea

check the answers

3.66-3.2= .46

5-3.66= 1.34

1.34/.46= 134/46 = 67/23

=74 4/9/25 5/9= 670/230 = 67/23

check the answers the usual way:

5x +3.2y= 5(25 5/9) + 3.2(74 4/9)

= 5(230/9) + 3.2(670/9)

= 1150/9+ 2144/9

= 3294/9=366

100(3.66) = 366

9) .6x + 0y = .4(x+y) where x= Liters of 60%, y=Liters of water added to get x+y Liters of 40%

.6x =.4x +.4y

.2x =.4y

x =2y

.4(x+y)=.4(2y+y) =.4(3y)=1.2y

1.2y = .3(3y+1)

.3y =.3

y=1 Liter water added to 2 Liters 60% to get 3 Liters 40%

then add 1 more liter water to get 4 Liters 30%

You end up with 4 Liters of 30% solution