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).

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°

the answer is 99.