Solve the system of linear equation by adding or subtracting : x+y=5 , x-3=3

Subtract

x + y = 5

-(x - 3y = 3)

4y = 2

Isolate the y. Divide 4 from both sides

4y/4 = 2/4

y = 1/2

y = 1/2

Plug in 1/2 for y in one of the equations.

x + y = 5

x + (1/2) = 5

Isolate the x. Subtract 1/2 from both sides

x + 1/2 (-1/2) = 5 (-1/2)

x = 4 1/2

x = 4 1/2, y = 1/2, is your answer

hope this helps

Answers

x = 4 1/2

y = 1/2

Explanation

x + y = 5 (i)

x - 3y = 3 (ii)

By substitution method, first make x the subject from equation (i)

x + y = 5

x = 5 - y

Substitute x in equation (ii) with 5-y.

x - 3y = 3

(5-y) - 3y = 3

5 - y - 3y = 3

5 - 4y = 3

4y = 5-3

4y = 2

y = 2/4 = 1/2

From equation (i),

x = 5 - y

= 5 - 1/2

= 4 1/2

{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

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