Part A: Write the equation that represents M.
$$y=2x-5$$
Write the equation that represents N.
$$y=3x+2$$
( that is right^^^^^)
Part B: Using the equations you wrote in part A find the point where the lines M and N intersect. show your work
I used the substitution method and got $(7,9)$
(Don't know if this is correct^^^^^)
Part C: Write the equation of a line that passes through both the intersection point found in Part B and the origin. Explain your equation or show your work.
( i have no idea how to do this???^^^^^^)
Note: The system of linear equations ${y=2x-5, y=3x+2}$ does not have $(7,9)$ as a solution since $3*7 + 2 = 23$ which is not $9.$
Part B) Substitution method will yield
$2x-5 = 3x+2.$
One can solve this equality for $x$ and find $x = -7$
Go back to either $M$ or $N$ to find $y$. They will be the same in both equations if your algebra is correct in the substitution method.
$2(-7)-5 = -19.$
Check this in equation $N$ to ensure correctness.
$3(-7)+2= -19.$ So $(-7,-19)$ is the point of intersection for the system.
Part C) Here we compute the line through the points $(-7,-19)$ and $(0,0)$. The slope is $\frac{-19}{-7}$, or $\frac{19}{7}$. Since the line goes through the origin, the $y$ intercept is zero and the equation is
$y=\frac{19}{7}x$