How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent #-3x=5-y# and #2y=6x+10#?

1 Answer
Jul 24, 2018

Answer:

Please see below.

Explanation:

Just draw the graphs of the two linear equations in two variables representing lines

  1. If the two lines intersect, the point of intersection is the solution. In such a case we have a consistent solution.

  2. If the two lines are parallel, they do not intersect and hence there is no solution. In such a case, we also say equations are inconsistent .

  3. In the present case observe that #-3x=5-y# and moving #x# and #y# on opposite sides, we get #y=5+3x# and multiplying each side by #2#, we get #2y=6x+10#, which is the equation of the other line.

Hence, the two equations represent the same line. In such a case one can say that the two lines are coincident i.e. they intersect at infinite solutions represented by #(t,5+3t)#.

graph{5+3x [-20, 20, -10, 10]}