Question

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`?

Answer 1

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]}