Solve each system by substitution.
-
y = 6x – 11
-2x – 3y=-7

Point form (2.1)

Equation form: x=2,y=1

(2, 1 )

Step-by-step explanation:

y = 6x - 11 → (1)

- 2x - 3y = - 7 → (2)

Substitute y = 6x - 11 into (2)

- 2x - 3(6x - 11) = - 7 ← distribute parenthesis and simplify left side

- 2x - 18x + 33 = - 7

- 20x + 33 = - 7 ( subtract 33 from both sides )

- 20x = - 40 ( divide both sides by - 20 )

x = 2

Substitute x = 2 into (1)

y = 6(2) - 11 = 12 - 11 = 1

solution is (2, 1 )

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction

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