Question

solve the system using the substitution method. if the system does not have one unique solution, also state the number of solutions and whether the system is inconsistent or the equations are dependent. express numbers in exact simplified form.
7x - y=-13
-2y=-14x + 14
the system has one solution.
the solution set is {(box,box)}.
the system has no solution, {}.
the system is inconsistent.
the equations are dependent.
the system has infinitely many solutions.
the solution set is {(x,y)|box}.
the system is inconsistent.
the equations are dependent.

Explanation:

Step1: Rearrange the first - equation for y

From $7x - y=-13$, we get $y = 7x + 13$.

Step2: Simplify the second - equation

Starting with $-2y=-14x + 14$, divide both sides by $-2$ to get $y = 7x-7$.

Step3: Set the two expressions for y equal to each other

$7x + 13=7x-7$.
Subtract $7x$ from both sides: $7x-7x + 13=7x-7x-7$, which simplifies to $13=-7$. This is a contradiction.

Answer:

The system has no solution, {}. The system is inconsistent.