Determine if Dependent, Independent, or Inconsistent 8x-y=3 , y=8x-3

$8 x - y = 3$ , $y = 8 x - 3$

Solve the system of equations.

Move all terms containing variables to the left side of the equation.

Subtract $8 x$ from both sides of the equation.

$y - 8 x = - 3$

$8 x - y = 3$

Reorder $y$ and $- 8 x$ .

$- 8 x + y = - 3$

$8 x - y = 3$

$- 8 x + y = - 3$

$8 x - y = 3$

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

Since $0 = 0$ , the equations intersect at an infinite number of points.

Infinite number of solutions

Solve one of the equations for $y$ .

Subtract $8 x$ from both sides of the equation.

$- y = 3 - 8 x$

Divide each term in $- y = 3 - 8 x$ by $- 1$ and simplify.

Divide each term in $- y = 3 - 8 x$ by $- 1$ .

$\frac{- y}{- 1} = \frac{3}{- 1} + \frac{- 8 x}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{3}{- 1} + \frac{- 8 x}{- 1}$

Divide $y$ by $1$ .

$y = \frac{3}{- 1} + \frac{- 8 x}{- 1}$

Simplify the right side.

Simplify each term.

Divide $3$ by $- 1$ .

$y = - 3 + \frac{- 8 x}{- 1}$

Move the negative one from the denominator of $\frac{- 8 x}{- 1}$ .

$y = - 3 - 1 \cdot (- 8 x)$

Rewrite $- 1 \cdot (- 8 x)$ as $- (- 8 x)$ .

$y = - 3 - (- 8 x)$

Multiply $- 8$ by $- 1$ .

$y = - 3 + 8 x$

The solution is the set of ordered pairs that make $y = - 3 + 8 x$ true.

$(x, - 3 + 8 x)$

Since the system is always true, the equations are equal and the graphs are the same line. Thus, the system is dependent.

Dependent