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] " . ___________________________________________________________
We would put 1/2 for the half-circle because its half of a circle. And we square it because where finding area. The middle is square, and the two up top is half a circle. Hope that helps :D
