Use the substitution method to solve the system of equations. choose the correct ordered pair.
3x- y=3
y=2x +2

a. (2,6)
b. (5,12)
c. (4,10)
d.(3,8)

Explanation:

Start with the first equation. We'll plug in y = 2x+2

3x - y = 3

3x - ( y ) = 3

3x - ( 2x+2 ) = 3 replace y with 2x+2

3x - 2x - 2 = 3 distribute the negative through to all terms inside

x-2 = 3   combine like terms

x-2+2 = 3+2 add 2 to both sides

x = 5

Use this x value to find the value of y. The easiest equation to use is the one in which y is already isolated for us

y = 2x+2

y = 2*5+2 replace x with 5

y = 10+2

y = 12

Though we can use the other equation as well

3x-y = 3

3*5-y = 3 replace x with 5

15 - y = 3

15-y-15 = 3-15 subtract 15 from both sides

-y = -12

y = 12 multiply both sides by -1, or change the signs of both sides

We get the same result for y.

The solution is (x,y) = (5,12) meaning that the graphs of the two original equations cross at this point.

this answer is !

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;