Which is the best approximation for the solution of the system of equations? y=-2/5x+1 y=3x-2

x = 15/17  , y = 11/17

Step-by-step explanation:

Solve the following system:

{y = 1 - (2 x)/5 | (equation 1)

{y = 3 x - 2 | (equation 2)

Express the system in standard form:

{(2 x)/5 + y = 1 | (equation 1)

{-(3 x) + y = -2 | (equation 2)

Swap equation 1 with equation 2:

{-(3 x) + y = -2 | (equation 1)

{(2 x)/5 + y = 1 | (equation 2)

Add 2/15 × (equation 1) to equation 2:

{-(3 x) + y = -2 | (equation 1)

{0 x+(17 y)/15 = 11/15 | (equation 2)

Multiply equation 2 by 15:

{-(3 x) + y = -2 | (equation 1)

{0 x+17 y = 11 | (equation 2)

Divide equation 2 by 17:

{-(3 x) + y = -2 | (equation 1)

{0 x+y = 11/17 | (equation 2)

Subtract equation 2 from equation 1:

{-(3 x)+0 y = -45/17 | (equation 1)

{0 x+y = 11/17 | (equation 2)

Divide equation 1 by -3:

{x+0 y = 15/17 | (equation 1)

v0 x+y = 11/17 | (equation 2)

Collect results:

{x = 15/17  , y = 11/17

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;