Select the correct answer. What is the solution to this system of equations?
x - 2y = 15
2x + 4y=-18
O A. x= 1, y= -6
B.
x= 1, y=-7
C. x= 3, y=-6
D. x= 3. y=-7
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A. x=3, y= -6

Step-by-step explanation:

x - 2y = 15

2x + 4y= -18

Solving for x

x-2y=15

Subtract x from both sides

-2y= -x+15

Multiply both sides by -1

2y=x-15

Multiply both sides by 2

4y=2x-30

2x+4y= -18

Subtract 2x from both sides

4y= -2x-18

Combine equations:

-2x-18=2x-30

Add 2x to both sides

-18=4x-30

Add 30 to both sides

12=4x

4x=12

Divide both sides by 4

x=3

Solving for y

x-2y=15

Add 2y to both sides

x=2y+15

Multiply both sides by 2

2x=4y+30

2x + 4y= -18

Subtract 4y from both sides

2x= -4y-18

Combine equations:

-4y-18=4y+30

Add 4y to both sides

-18=8y+30

Subtract 30 from both sides

8y= -48

Divide both sides by 8

y= -6

so, converting firstly the mixed fractions to improper fractions and then "adding".

for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

then, given the following line:

so,

we are looking for m_ {2}:

then, the line is given by:

we find "b" replacing the given point:

finally, the equation is:

option c