The solution set for 6a2 - a -5 = 0 is

see explanation

Step-by-step explanation:

Given

6a² - a - 5 = 0

Consider the factors of the product of the a² term and the constant term which sum to give the coefficient of the a- term.

product = 6 × - 5 = - 30 and sum = - 1

The factors are - 6 and + 5

Use these factors to split the a- term

6a² - 6a + 5a - 5 = 0 ( factor the first/second and third/fourth terms )

6a(a - 1) + 5(a - 1) = 0 ← factor out (a - 1) from each term

(a - 1)(6a + 5) = 0

Equate each factor to zero and solve for a

a - 1 = 0 ⇒ a = 1

6a + 5 = 0 ⇒ 6a = - 5 ⇒ a = -

Solution set = { 1, - }

step-by-step explanation:

{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