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.
-280x - 115y = 970
y - 10 = -16

the system has one solution.
the solution set is {()}.
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) | }.
the system is inconsistent.
the equations are dependent.

Explanation:

Step1: Solve the second - equation for y

Solve $y - 10=-16$ for $y$. Add 10 to both sides of the equation:
$y=-16 + 10=-6$

Step2: Substitute y into the first - equation

Substitute $y = - 6$ into $-280x-115y = 970$. We get $-280x-115\times(-6)=970$.
First, calculate $-115\times(-6)=690$. Then the equation becomes $-280x + 690=970$.
Subtract 690 from both sides: $-280x=970 - 690=280$.
Divide both sides by - 280: $x=\frac{280}{-280}=-1$.

Answer:

The system has one solution.
The solution set is $\{(-1,-6)\}$