We have the point #(3, 5)# that will be a point on both lines in the system of equations.
We can then just pick two slopes. I will pick:
We can now use the point slope formula to write the two equations:
The point-slope form of a linear equation is: #(y - color(blue)(y_1)) = color(red)(m)(x - color(blue)(x_1))#
Where #(color(blue)(x_1), color(blue)(y_1))# is a point on the line and #color(red)(m)# is the slope.
#(y - color(blue)(y_1)) = color(red)(m)(x - color(blue)(x_1))# becomes:
#(y - color(blue)(5)) = color(red)(2)(x - color(blue)(3))#
#(y - color(blue)(y_1)) = color(red)(m)(x - color(blue)(x_1))# becomes:
#(y - color(blue)(5)) = color(red)(-1/3)(x - color(blue)(3))#
If, necessary, we can convert them to slope-intercept form:
#y - color(blue)(5) = (color(red)(2) xx x) - (color(red)(2) xx color(blue)(3))#
#y - color(blue)(5) = 2x - 6#
#y - color(blue)(5) + 5 = 2x - 6 + 5#
#y = 2x - 1#
#y - color(blue)(5) = (color(red)(-1/3) xx x) - (color(red)(-1/3) xx color(blue)(3))#
#y - color(blue)(5) = -1/3x - (-1)#
#y - color(blue)(5) = -1/3x + 1#
#y - color(blue)(5) + 5 = -1/3x + 1 + 5#
#y = -1/3x + 6#