State the number of solutions of the system of linear equations $\left\{ \begin{array} { l }
y = 3 x - 7 \
y = 7 x - 3
\end{array} \right.$ without solving the system.
A)infinitely many solutions
B)one solution
C)no solution

Question

State the number of solutions of the system of linear equations $\left\{ \begin{array} { l } 
y = 3 x - 7 \
y = 7 x - 3
\end{array} \right.$ without solving the system.
A)infinitely many solutions
B)one solution
C)no solution

Quizplus · Accepted Answer

Since both equations are in the form y = mx + b, they each represent a line with a unique slope (m) and y-intercept (b). The fact that the two equations have different slopes means that they represent two different lines in the coordinate plane. The fact that they have different y-intercepts means that these two lines do not intersect at any point in the coordinate plane. Therefore, there is no solution to the system of equations.

State the Number of Solutions of the System of Linear {y=3x−7y=7x−3\left\{ \begin{array} { l } y = 3 x - 7 \\y = 7 x - 3\end{array} \right.{y=3x−7y=7x−3​

State the Number of Solutions of the System of Linear $\left\{ \begin{array} { l } y = 3 x - 7 \\y = 7 x - 3\end{array} \right.$