Solve the equations using substitution

7x-2y=3

14x+y=14

x = 31/35, y = 8/5

Step-by-step explanation:

Solve the following system:

{7 x - 2 y = 3

14 x + y = 14

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

In the second equation, look to solve for y:

{7 x - 2 y = 3

14 x + y = 14

Hint: | Solve for y.

Subtract 14 x from both sides:

{7 x - 2 y = 3

y = 14 - 14 x

Hint: | Perform a substitution.

Substitute y = 14 - 14 x into the first equation:

{7 x - 2 (14 - 14 x) = 3

y = 14 - 14 x

Hint: | Expand the left hand side of the equation 7 x - 2 (14 - 14 x) = 3.

7 x - 2 (14 - 14 x) = (28 x - 28) + 7 x = 35 x - 28:

{35 x - 28 = 3

y = 14 - 14 x

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

In the first equation, look to solve for x:

{35 x - 28 = 3

y = 14 - 14 x

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

Add 28 to both sides:

{35 x = 31

y = 14 - 14 x

Hint: | Solve for x.

Divide both sides by 35:

{x = 31/35

y = 14 - 14 x

Hint: | Perform a back substitution.

Substitute x = 31/35 into the second equation:

Answer: {x = 31/35, y = 8/5