Lucy correctly answered 70% of the questions on her science homework. she counted 14 correct answers on her paper .if each question is of a equal value ,how many questions did lucy have on her science homework

Lucy has 20 questions in her science home work

Solution:

Given that,

Lucy correctly answered 70% of the questions on her science homework

She counted 14 correct answers on her paper

To find: Number of questions in her science home work

Let "x" be the number of questions in her science home work

From given we can say,

Lucy correctly answered 70% of questions

She counted 14 correct answers

70 % of total questions = 14 correct answers

70 % of x = 14

Thus Lucy has 20 questions in her science home work

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1