Answer:
(-7.4, 12.8) OR (-111/15 , 192/15)
x = -7.4 OR -111/15
y = 12.8 OR -192/15
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).