CAYB is a quadrilateral CA= 3a
CB= 6b
BY= 5a-b

X is the point on AB such that AX:XB= 1:2

Prove that CX = 2/5 CY

see explanation

Step-by-step explanation:

CY = CB + BY

     = 6b + 5a - b

     = 5a + 5b

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CX = CA + AX

     = CA + AB , find AB

AB = AC + CB

     = - 3a + 6b

     = 6b - 3a

Thus

CX = CA  + AB

      = 3a + (6b - 3a)

      = 3a + 2b - a

      = 2a + 2b

---------------------

and

CY

= (5a + 5b)

= 2a + 2b = CX

Hence CX = CY ⇒ Proven

(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