What is the solution to this system of equations?

3x-2y=5
x+2y=7

x=_, y=_

Step 1) Solve the second equation for

x

:

x

+

3

y

=

−

5

x

+

3

y

−

3

y

=

−

5

−

3

y

x

+

0

=

−

5

−

3

y

x

=

−

5

−

3

y

Step 2) Substitute

−

5

−

3

y

for

x

in the first equation and solve for

y

:

3

(

−

5

−

3

y

)

−

2

y

=

7

−

15

−

9

y

−

2

y

=

7

−

15

−

11

y

=

7

15

−

15

−

11

y

=

15

+

7

0

−

11

y

=

22

−

11

y

=

22

−

11

y

−

11

=

22

−

11

−

11

y

−

11

=

−

2

y

=

−

2

Step 3) Substitute

−

2

for

y

in the solution to the second equation at the end of Step 1 and calculate x:

x=−5−(3×−2)

x=−5−(−6)

x=−5+6

x=1

The solution is x=1 and y=−2

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