How do you solve 2x-3y=-4 and x+3y=7 by substitution

x = 1, y = 2

Step-by-step explanation:

Solve the following system:

{2 x - 3 y = - 4

x + 3 y = 7

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

In the second equation, look to solve for x:

{2 x - 3 y = - 4

x + 3 y = 7

Hint: | Solve for x.

Subtract 3 y from both sides:

{2 x - 3 y = - 4

x = 7 - 3 y

Hint: | Perform a substitution.

Substitute x = 7 - 3 y into the first equation:

{2 (7 - 3 y) - 3 y = - 4

x = 7 - 3 y

Hint: | Expand the left hand side of the equation 2 (7 - 3 y) - 3 y = - 4.

2 (7 - 3 y) - 3 y = (14 - 6 y) - 3 y = 14 - 9 y:

{14 - 9 y = - 4

x = 7 - 3 y

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

In the first equation, look to solve for y:

{14 - 9 y = - 4

x = 7 - 3 y

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

Subtract 14 from both sides:

{-9 y = - 18

x = 7 - 3 y

Hint: | Solve for y.

Divide both sides by - 9:

{y = 2

x = 7 - 3 y

Hint: | Perform a back substitution.

Substitute y = 2 into the second equation:

{y = 2

x = 1

Hint: | Sort results.

Collect results in alphabetical order:

Answer: {x = 1, y = 2