Louisa states that the solution to the equation One-fourth x minus 3 = StartFraction 3 Over 8 EndFraction x + 4 is x = 56. She verifies her solution using the steps below. Equation: One-fourth x minus 3 = StartFraction 3 Over 8 EndFraction x + 4 Step 1: One-fourth (56) minus 3 = StartFraction 3 Over 8 EndFraction (56) + 4 Step 2: 14 minus 3 = 21 + 4 Step 3: 11 = 25 Which statement most accurately describes Louisa's error? Louisa made an error when determining the original solution of x = 56. Louisa made an error when substituting the solution in for x. Louisa made an error when multiplying 56 by One-fourth and by StartFraction 3 Over 8 EndFraction. Louisa made an error when adding or subtracting.

Given:

The equation is

To find:

The Louisa's mistake.

Solution:

We have,

Multiply both sides by 8.

Louisa made an error when determining the original solution of x = 56.

Therefore, the correct option is A.

{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