4if alice gives susan £6.00 the money they each have is in the
ratio 2: 1; however, if susan gives alice £1.00 the ratio is 1: 3.
how much money have alice and susan each before they
exchange any money?

Alice and Susan have  £62 and  £22 respectively before the exchange.

Step-by-step explanation:

Let

A =Alice's total amount before exchange

S= Susan's total amount before exchange

if Alice gives Susan  £6.00 and ratio become 2:1

Then  (A-6)/(S+6) = 2/1

A-2S=18     eqn(1)

if Susan gives Alice  £1.00 and ration becomes 3:1

then (A+1)/(S-1) =3/1

3A-S= -4    eqn (2)

solving eqn(1) and eqn(2) simultaneously

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3