$x^2+y^2=225 \\
x-7y=-75 \\ \\
\hbox{solve the second equation for x:} \\
x-7y=-75 \ \ \ |+7y \\
x=7y-75 \\ \\
\hbox{substitute 7y-75 for x in the first equation:} \\
(7y-75)^2+y^2=225 \\
49y^2-1050y+5625+y^2=225 \\
50y^2-1050y+5625=225 \ \ \ \ \ \ \ \ \ |-225 \\
50y^2-1050y+5400=0 \ \ \ \ \ \ \ \ \ \ \ \ |\div 50 \\
y^2-21y+108=0 \\
y^2-9y-12y+108=0 \\
y(y-9)-12(y-9)=0 \\
(y-12)(y-9)=0 \\
y-12=0 \ \lor \ y-9=0 \\
y=12 \ \lor \ y=9$

$x=7y-75 \\
x=7 \times 12 -75 \ \lor \ x=7 \times 9-75 \\
x=84-75 \ \lor \ x=63-75 \\
x=9 \ \lor \ x=-12 \\ \\
(x,y)=(9,12) \hbox{ or } (x,y)=(-12,9)$

The points are (9,12) and (-12,9).
The answer is A.

7 0

3 years ago

What is the solution to the equation below? 5 - n/2 = 12

Zarrin [17]

Step-by-step explanation:

5 - n/2 = 12

10/2 - n/2 = 12

n = (12 × (-2)) + 10

n = (-24) + 10

n = -14

Let's prove it :

$5 - ( - \frac{14}{2} ) \\ = \frac{10}{2} + \frac{14}{2} \\ = \frac{24}{2} \\ = 12$

Conclusion :

5 - n/2 = 12

5 - (-14/2) = 12

and

n = -14

8 0

3 years ago

Standard form of 10-⁹

zavuch27 [327]

Answer: 1/1000000000

Step-by-step explanation:

5 0

3 years ago