Shiloh is 7 years older than courtney. shiloh's age is 13 years less than two times courtney's age. the system below models the relationship between shiloh's age (s) and courtney's age (c):

s = c + 7
s = 2c – 13

which of the following methods is correct to find shiloh's and courtney's age? (4 points)

solve s + 7 = 2s – 13 to find the value of s.
solve c + 7 = 2c – 13 to find the value of c.
write the points where the graphs of the equations intersect the x-axis.
write the points where the graphs of the equations intersect the y-axis.

Option B is correct

Solve c + 7 = 2c – 13 to find the value of c.

Step-by-step explanation:

As per the statement:

Shiloh is 7 years older than Courtney. Shiloh's age is 13 years less than two times Courtney's age.

The system below models the relationship between Shiloh's age (s) and Courtney's age (c):

          ....[1]

        ....[2]

Equate the equation [1] and [2], to solve for c we have;

Therefore, the following methods is correct to find Shiloh's and Courtney's age is:

Solve c + 7 = 2c – 13 to find the value of c.

(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