Write each equation in slope-intercept form. Without graphing the equations, state whether the system of equations is
consistent, inconsistent, or dependent. Also indicate whether the system has exactly one solution, no solution, or an
infinite number of solutions.
-$$\begin{array} { c }
x + 3 y = 3 \
8 x - 5 y = - 5
\end{array}$$
A)inconsistent
B)dependent
C)consistent no solution infinite number of solutions one solution

Question

Write each equation in slope-intercept form. Without graphing the equations, state whether the system of equations is
consistent, inconsistent, or dependent. Also indicate whether the system has exactly one solution, no solution, or an
infinite number of solutions.
-$$\begin{array} { c } 
x + 3 y = 3 \
8 x - 5 y = - 5
\end{array}$$
A)inconsistent
B)dependent
C)consistent no solution infinite number of solutions one solution

Quizplus · Accepted Answer

The equations in slope-intercept form are $y = -\frac{1}{3}x + 1$ and $y = \frac{8}{5}x - 1$. Since the slopes are different ($-\frac{1}{3} \neq \frac{8}{5}$), the lines are not parallel and not the same line, indicating they will intersect at exactly one point. Therefore, the system is consistent and has exactly one solution.

Write Each Equation in Slope-Intercept Form x+3y=38x−5y=−5\begin{array} { c } x + 3 y = 3 \\8 x - 5 y = - 5\end{array}x+3y=38x−5y=−5​

Write Each Equation in Slope-Intercept Form $\begin{array} { c } x + 3 y = 3 \\8 x - 5 y = - 5\end{array}$