solve the system of equations and choose the correct ordered pair for x + 3y equals 6 + 7 x + 6 y equals 31

(-7.4, 12.8) OR (-111/15, 192/15)

x = - 7.4 OR - 111/15

y = 12.8 OR - 192/15

Step-by-step explanation:

Write the problem in algebraic form

x + 3y = 6 + 7 x + 6y = 31

Split the equation so you have two of them

x + 3y = 31

6 + 7 x + 6y = 31

Notice that x + 3y = 31 can easily be arranged to isolate the variable "x".

x = 31 - 3y

Substitute x for 31-3y in the other equation

6 + 7 x + 6y = 31

6 + 7 (31 - 3y) + 6y = 31 Distribute. Multiply numbers outside bracket with inside

6 + 217 - 21y + 6y = 31 Combine like terms (terms with same variables)

6 + 217 - 15y = 31 Combine the like terms that have no variables

223 - 15y = 31 Start isolating "y". Do reverse operations

223 - 223 - 15y = 31 - 223 Subtract 223 from both sides

-15y = - 192

-15y/-15 = - 192/-15 Divide both sides by - 15

y = 192/15 Answer for y in fractional form

y = 12.8 Answer for y in decimal form

Substitute "y" for 192/15 OR 12.8 in any equation to find "x". I will use fractional form to get "y" in both fractional and decimal form.

x + 3y = 31

x + 3 (192/15) = 31 Multiply to simplify

x + 576/15 = 31

x + 576/15 - 576/15 = 31 - 576/15 Subtract 576/15 from both sides

x = - 111/15 Answer for x in fractional form

x = - 7.4 Answer for x in decimal form

Therefore the solution is (-7.4, 12.8) or (192/15, - 111/15).