Create a system of equations with a solution of (5,-2)

Solution:

Given that,

create a system of equations with a solution of (5,-2)

The equation for a line in slope intercept form:

y = mx + b

Where, m is the slope and b is the y intercept

For (x, y) = (5, -2)

-2 = 5m + b

When m = 5

-2 = 5(5) + b

-2 = 25 + b

b = -2 - 25

b = -27

When m = -2

-2 = 5(-2) + b

-2 = -10 + b

b = 8

Thus equations are:

y = 5x - 27

y = -2x + 8

Rearranging to standard form,

5x - y = 27 --- eqn 1

2x + y = 8 eqn 2

Thus the system of equations are found

Solve eqn 1 and eqn 2

Add both eqn 1 and eqn 2

7x = 35

Substitute x = 5 in eqn 2

2(5) + y = 8

y = 8 - 10

Thus solution is (5, -2) and the found system of equations are correct

the answer to this question is yes

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.