9514 1404 393
Answer:
30x +25y = 148
Explanation:
We can use substitution to find the point of intersection of ...
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