The given system of equations are consistent and independent
Solution:
Given system of equations are:
y = 6x - 7 ----- eqn 1
y = -3x + 8 -------- eqn 2
We have to classify the given system of equations
Let us first solve both the equations
Substitute eqn 2 in eqn 1
-3x + 8 = 6x - 7
Move the variables to one side and constants to other side
[tex]-3x - 6x = -7 - 8\\\\-9x = -15\\\\9x = 15\\\\x = \frac{15}{9}\\\\x = \frac{5}{3}[/tex]
Now substitute the above value of "x" in eqn 1
[tex]y = 6 \times \frac{5}{3} - 7\\\\y = 10 - 7\\\\y = 3[/tex]
Thus the given system of equations has only one solution [tex](x, y) = (\frac{5}{3}, 3)[/tex]
If a system has at least one solution, it is said to be consistent.
If a consistent system has exactly one solution, it is independent
So the given system of equations are consistent and independent
