Question

Classify the linear system shown on the graph. What is the correct classification?

Answer 1

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

$-3x - 6x = -7 - 8\\\\-9x = -15\\\\9x = 15\\\\x = \frac{15}{9}\\\\x = \frac{5}{3}$

Now substitute the above value of "x" in eqn 1

$y = 6 \times \frac{5}{3} - 7\\\\y = 10 - 7\\\\y = 3$

Thus the given system of equations has only one solution $(x, y) = (\frac{5}{3}, 3)$

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