The relationship between two numbers is described below, where x represents the first number and y represents the second number. the square of the first number is equal to the sum of the second number and 16. the difference of 4 times the second number and 1 is equal to the first number multiplied by 7. select the equations that form the system that models this situation. then, select the solution(s) of the system. equations solutions y2 + 16 = x (2x)2 = y + 16 (1,15) (5,9) x2 = y + 16 7y - 1 = 4x (2,-12) (8,48) 1 - 4y = 7x 4y - 1 = 7x (4,-7) (9,3) nextreset

x^2=y+16

4y-1=7x

(5,9)

Step-by-step explanation:

The condition says:

The square of first number is equal to the sum of the second number and 16:

Lets say that the first number is 'x' and the second number is 'y'. So the square of 'x' is and that is equal to the sum of second number i.e y and 16:

Second condition says that:

The difference of 4 times the second number and 1 is equal to the first number multiplied by 7:

4 times the second number is and difference of 1 is:

and this is equal to 7 times the first number:  

So the two equations are:

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true