6. John is six years older than his sister Ella. Three times Ella’s age less two times John’s age is 13. Define appropriate variable(s) and write equation(s) to represent the situation. Solve to find John and Ella’s ages. Show all work and write a
conclusion.

John is 31

Ella is 25

Step-by-step explanation:

Let sister's age be x, then John's age is (x + 6). So from sentence 2,

(3x) - 2(x + 6) = 13

3x - 2x - 12 = 13

x = 13 + 12 = 25

and x + 6 = 31

(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