Question

The first line in a system of linear equations has a slope of 3 and passes through the point (-1 , -8). The second line passes through the points (-6 , 3) and (10 , -1).

What is the solution to the system?

Answer 1

The equation of the first line can be written in point-slope form as
.. y = 3(x +1) -8
or
.. 3x -y = 5

The equation of the second line can be written in 2-point form as
.. y = (-1-3)/(10-(-6))*(x +6) +3
.. y = (-1/4)(x +6) +3
or
.. x +4y = 6

A graph shows the solution to this system is (x, y) = (2, 1).

_____
The second equation can be used to write an expression for x:
.. x = 6 -4y
This can be substituted into the first equation.
.. 3(6 -4y) -y = 5
.. 18 -13y = 5 . . . . . . . collect terms
.. 13 = 13y . . . . . . . . . add 13y-5
.. 1 = y . . . . . . . . . . . . divide by 13
From the above equation for x
.. x = 6 -4*1 = 2