Answer: x is, 2 6 8 10 20-- i think
Step-by-step explanation: y is, 2 3 4 6 10
18 inches or 1 foot and 6 inches
multiply 3 feet by 12 and add two to get the width of the door in inches then subtract 20 inches from it to get the difference
The correct answer is: [B]: " (2, 5) ".
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Given:
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-5x + y = -5 ;
-4x + 2y = 2 .
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Consider the first equation:
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-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".
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y - 5x + 5x = -5 + 5x
y = -5 + 5x ; ↔ y = 5x - 5 ;
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Now, take our second equation:
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-4x + 2y = 2 ; and plug in "(5x - 5)" for "y" ; and solve for "x" :
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-4x + 2(5x - 5) = 2 ;
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Note, 2(5x - 5) = 2(5x) - 2(5) = 10x - 10 ;
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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 ;
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Now, take our first given equation; and plug our solved value for "x" ; which is "2" ; and solve for "y" ;
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-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 .
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So, we have, x = 2 ; and y = 5 .
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Now, let us check our work by plugging in "2" for "x" and "5" for "y" in BOTH the original first and second equations:
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first equation:
-5x + y = -5 ;
-5(2) + 5 =? -5?
-10 + 5 =? -5 ? YES!
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second equation:
-4x + 2y = 2 ;
-4(2) + 2(5) =? 2 ?
-8 + 10 =? 2 ? Yes!
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So, the answer is:
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x = 2 , y = 5 ; or, "(2, 5)" ; which is: "Answer choice: [B] " .
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![\vec{BE}=[-2-(-6);\ 4-10]=[4;\ -6]](https://tex.z-dn.net/?f=%5Cvec%7BBE%7D%3D%5B-2-%28-6%29%3B%5C%204-10%5D%3D%5B4%3B%5C%20-6%5D)
![D(x;\ y)\\\\\vec{ED}=[x-(-2);\ y-4]=[x+2;\ y-4]\\\\\vec{ED}=\vec{BE}\ therefore\\\\ \ [x+2;\ y-4]=[4;\ -6]\to x+2=4\ and\ y-4=-6\\\\x=2\ and\ y=-2\\\\Answer:\ \boxed{A.\ (2;\ -2)}](https://tex.z-dn.net/?f=D%28x%3B%5C%20y%29%5C%5C%5C%5C%5Cvec%7BED%7D%3D%5Bx-%28-2%29%3B%5C%20y-4%5D%3D%5Bx%2B2%3B%5C%20y-4%5D%5C%5C%5C%5C%5Cvec%7BED%7D%3D%5Cvec%7BBE%7D%5C%20therefore%5C%5C%5C%5C%20%5C%20%5Bx%2B2%3B%5C%20y-4%5D%3D%5B4%3B%5C%20-6%5D%5Cto%20x%2B2%3D4%5C%20and%5C%20y-4%3D-6%5C%5C%5C%5Cx%3D2%5C%20and%5C%20y%3D-2%5C%5C%5C%5CAnswer%3A%5C%20%5Cboxed%7BA.%5C%20%282%3B%5C%20-2%29%7D)
