Two angles are supplementary, and one angle is one-fifth the other. Find the measure of the two angles.
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Answer: (12, 5)
Step-by-step explanation:
3x + 2y = 46 x + y = 17
Subtract y from both sides of the equation.
x = 17 − y 3x + 2y = 46
Replace all occurrences of x with 17 − y in each equation.
51 − y = 46
x = 17 − y
Solve for y in the first equation.
Move all terms not containing y to the right side of the equation.
Subtract 51 from both sides of the equation.
−y = 46 − 51
x = 17 − y
Subtract 51 from 46.
−y = −5
x = 17 − y
Multiply each term in −y = −5 by −1
Multiply each term in −y = −5 by −1. (−y) ⋅ −1 = (−5) ⋅ −1
x = 17 − y
Multiply (−y) ⋅ −1.
y = (−5) ⋅ −1
x = 17 − y
Multiply −5 by −1.
y = 5
x = 17 − y
Replace all occurrences of y with 5 in each equation.
Replace all occurrences of y in x = 17 − y with 5. x = 17 − (5)
y = 5
Simplify 17 − (5).
Multiply −1 by 5.
x = 17 − 5
y = 5
Subtract 5 from 17.
x = 12
y = 5
The solution to the system is the complete set of ordered pairs that are valid solutions.
(12, 5)
The result can be shown in multiple forms.
Point Form: (12, 5)
Equation Form: x = 12, y = 5
