5x - 2y = 3 -5x + 4y = 9 systems of equation

x = 3 , y = 6

Step-by-step explanation:

Solve the following system:

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

{4 y - 5 x = 9 | (equation 2)

Add equation 1 to equation 2:

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

{0 x+2 y = 12 | (equation 2)

Divide equation 2 by 2:

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

{0 x+y = 6 | (equation 2)

Add 2 × (equation 2) to equation 1:

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

{0 x+y = 6 | (equation 2)

Divide equation 1 by 5:

{x+0 y = 3 | (equation 1)

{0 x+y = 6 | (equation 2)

Collect results:

 {x = 3 , y = 6

6/20

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