Determine if Dependent, Independent, or Inconsistent 3x+y=-2 6x+2y=10

$3 x + y = - 2$ $6 x + 2 y = 10$

Solve the system of equations.

Multiply each equation by the value that makes the coefficients of $y$ opposite.

$(- 2) \cdot (3 x + y) = (- 2) (- 2)$

$6 x + 2 y = 10$

Simplify.

Simplify the left side.

Simplify $(- 2) \cdot (3 x + y)$ .

Apply the distributive property.

$- 2 (3 x) - 2 y = (- 2) (- 2)$

$6 x + 2 y = 10$

Multiply $3$ by $- 2$ .

$- 6 x - 2 y = (- 2) (- 2)$

$6 x + 2 y = 10$

$- 6 x - 2 y = (- 2) (- 2)$

$6 x + 2 y = 10$

$- 6 x - 2 y = (- 2) (- 2)$

$6 x + 2 y = 10$

Simplify the right side.

Multiply $- 2$ by $- 2$ .

$- 6 x - 2 y = 4$

$6 x + 2 y = 10$

$- 6 x - 2 y = 4$

$6 x + 2 y = 10$

$- 6 x - 2 y = 4$

$6 x + 2 y = 10$

Add the two equations together to eliminate $y$ from the system.

Since $0 \neq 14$ , there are no solutions.

No solution

Since the system has no solution, the equations and graphs are parallel and do not intersect. Thus, the system is inconsistent.

Inconsistent