Question

8.

Answer 1

9514 1404 393

Answer:

  30x +25y = 148

Step-by-step explanation:

We can use substitution to find the point of intersection of ...

• 3x +14 = 2y
• x + y = 6

Using the second equation, we can write an expression for y:

  y = 6 -x

Substituting that into the first equation gives ...

  3x +14 = 2(6 -x)

  3x +14 = 12 -2x . . . . . eliminate parentheses

  5x = -2 . . . . . . . . . . . add 2x-14

  x = -0.4 . . . . . . . . . divide by 5

  y = 6 -(-0.4) = 6.4

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Now, we want an equation for a line through the point (-0.4, 6.4) that is perpendicular to 5x = 6y+1

The perpendicular line will have the coefficients swapped with one of them negated. The constant will accommodate the given point.

  6x = -5y + c

  6(-0.4) +5(6.4) = c = 29.6

The perpendicular line can be written ...

  6x = -5y +29.6

In standard form, the equation is ...

  30x +25y = 148