How to solve system by substitution

X+y=10

X-y=2

x = 6, y = 4

Step-by-step explanation:

Solve the following system:

{x + y = 10

x - y = 2

Hint: | Choose an equation and a variable to solve for.

In the first equation, look to solve for y:

{x + y = 10

x - y = 2

Hint: | Solve for y.

Subtract x from both sides:

{y = 10 - x

x - y = 2

Hint: | Perform a substitution.

Substitute y = 10 - x into the second equation:

{y = 10 - x

2 x - 10 = 2

Hint: | Choose an equation and a variable to solve for.

In the second equation, look to solve for x:

{y = 10 - x

2 x - 10 = 2

Hint: | Isolate terms with x to the left hand side.

Add 10 to both sides:

{y = 10 - x

2 x = 12

Hint: | Solve for x.

Divide both sides by 2:

{y = 10 - x

x = 6

Hint: | Perform a back substitution.

Substitute x = 6 into the first equation:

{y = 4

x = 6

Hint: | Sort results.

Collect results in alphabetical order:

Answer: {x = 6, y = 4