Question 229937
Given the following system of linear equation, make comment about the lines and the number of solutions this system has.

y = -3x - 12  Equation A
y = 2x + 12   Equation B


Step 1.  The above lines in given in slope intercept form given as y=mx+b where m is the slope and b is the y-intercept when x=0 or at point (0,b).


Step 2.  The slope of Equation A is m1=-3 and the slope of Equation B is m2=2.  So they are not parallel since the parallel lines have the same slope.  The lines are not perpendicular since the product of their slopes is not equal to -1 since m1*m2 does not equal -1.


Step 3.  The lines intersect at a point so there is one solution.


Here's a graph of the two lines


{{{graph(600,600,-15,15,-15,15, -3x-12, 2x+12)}}}


The intersection between these two lines is given below using substituion:


*[invoke linear_substitution "x", "y", 3, 1, -12, -2, 1, 12]


Same results as before.


I hope the above steps and explanation were helpful. 


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Also, good luck in your studies and contact me at john@e-liteworks.com for your future math needs.


Respectfully, 
Dr J


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