# 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?

Jul 24, 2018

#### 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 $- 3 x = 5 - y$ and moving $x$ and $y$ on opposite sides, we get $y = 5 + 3 x$ and multiplying each side by $2$, we get $2 y = 6 x + 10$, 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 $\left(t , 5 + 3 t\right)$.

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