The correct answer is: [B]: " (2, 5) ". __________________________________________ Given: __________________________________________ -5x + y = -5 ; -4x + 2y = 2 . ___________________________________________ Consider the first equation: ___________________________ -5x + y = -5 ; ↔ y + (-5x) = -5 ;
↔y - 5x = -5 ; Add "5x" to each side of the equation; to isolate "y" on one side of the equation; and to solve in terms of "y". _____________________________________________ y - 5x + 5x = -5 + 5x
y = -5 + 5x ; ↔ y = 5x - 5 ; ____________________________________________ Now, take our second equation: ______________________________ -4x + 2y = 2 ; and plug in "(5x - 5)" for "y" ; and solve for "x" : _____________________________________________________ -4x + 2(5x - 5) = 2 ; ______________________________________________________ Note, 2(5x - 5) = 2(5x) - 2(5) = 10x - 10 ; __________________________________________ So: -4x + 10x - 10 = 2 ;
On the left-hand side of the equation, combine the "like terms" ;
-4x +10x = 6x ; and rewrite:
6x - 10 = 2 ;
Now, add "10" to each side of the equation:
6x - 10 + 10 = 2 + 10 ;
to get:
6x = 12 ; Now, divide EACH side of the equation by "6" ; to isolate "x" on one side of the equation; and to solve for "x" ;
6x/6 = 12 / 6 ;
x = 2 ; _________________________________ Now, take our first given equation; and plug our solved value for "x" ; which is "2" ; and solve for "y" ; _____________________________________ -5x + y = -5 ;
-5(2) + y = -5 ;
-10 + y = -5 ; ↔ y - 10 = -5 ;
Add "10" to each side of the equation; to isolate "y" on one side of the equation; and to solve for "y" ;
y - 10 + 10 = -5 + 10 ;
y = 5 . _____________________________ So, we have, x = 2 ; and y = 5 . ____________________________ Now, let us check our work by plugging in "2" for "x" and "5" for "y" in BOTH the original first and second equations: ______________________________ first equation:
-5x + y = -5 ;
-5(2) + 5 =? -5?
-10 + 5 =? -5 ? YES! ______________________ second equation:
-4x + 2y = 2 ;
-4(2) + 2(5) =? 2 ?
-8 + 10 =? 2 ? Yes! _______________________________________________________ So, the answer is: ___________________________________________________________ x = 2 , y = 5 ; or, "(2, 5)" ; which is: "Answer choice: [B] " . ___________________________________________________________
Your triangle is isosceles. You have been given the third angle, and you have been asked to find the measure of one of the two equal angles. We know that the internal angles of a triangle sum to 180, so
First turn 1/2 to 2/4 so you have a common denominator. Next turn the mixed numbers into improper fractions: 11 3/4 --> 47/4 and 8 2/4 --> 34/4 Subtract: 47/4 - 34/4 = 13/4 Divide: 13/4 = 3.25 3.25/2 --> 1.625 or 1 5/8 Therefore, he will have to place it 1 5/8 feet from each side
