Question

Solve the system using substitution. Show all work

Answer 1

Answer:

x = -2 , y = 3

Step-by-step explanation:

Solve the following system:

{4 x + 5 y = 7

y = 3 x + 9

Hint: | Perform a substitution.

Substitute y = 3 x + 9 into the first equation:

{4 x + 5 (3 x + 9) = 7

y = 3 x + 9

Hint: | Expand the left hand side of the equation 4 x + 5 (3 x + 9) = 7.

4 x + 5 (3 x + 9) = (15 x + 45) + 4 x = 19 x + 45:

{19 x + 45 = 7

y = 3 x + 9

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

In the first equation, look to solve for x:

{19 x + 45 = 7

y = 3 x + 9

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

Subtract 45 from both sides:

{19 x = -38

y = 3 x + 9

Hint: | Solve for x.

Divide both sides by 19:

{x = -2

y = 3 x + 9

Hint: | Perform a back substitution.

Substitute x = -2 into the second equation:

Answer:  {x = -2 , y = 3