How do you create a system of equation with a solution of (3,5)?

1 Answer
Jan 29, 2018

See a solution process below:

Explanation:

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:

  • First, Slope: #m_1 = 2#

  • Second Slope: #m_2 = -1/3#

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.

  • Equation 1:

#(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))#

  • Equation 2:

#(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:

  • Equation 1:

#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#

  • Equation 2:

#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#