Solve the linear equation
31x + 29y = 33
29x + 31y = 27

x = 2

y = -1

Step-by-step explanation:

Make the coefficient of x the same

Multiply the first equation by 29

31x + 29y = 33 becomes

899x + 841y = 957

Multiply the second equation by 31

29x + 31y = 27 becomes

899x + 961y = 837

Subtract the equations

(899x + 841y) - (899x + 961y) = 957 - 837

(899x - 899x) + (841y - 961y) = 120

841y - 961y = 120

-120y = 120

y = 120/-120 = -1

Substitute the value of y into both equations to find the value of x and check its right.

31x + 29y = 33

31x + 29(-1) = 33

31x - 29 = 33

31x = 33 + 29

31x = 62

x = 62/31 = 2

29x + 31y = 27

29x + 31(-1) = 27

29x - 31 = 27

29x = 27 + 31

29x = 58

x = 58/29 = 2

there is no question content here, but you for the free points! : d

{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