2 Answers

VPP · Answer 1 · 2021-12-02T06:24:48+0000

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

$-3x - 6x = -7 - 8\\\\-9x = -15\\\\9x = 15\\\\x = (15)/(9)\\\\x = (5)/(3)$

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

$y = 6 * (5)/(3) - 7\\\\y = 10 - 7\\\\y = 3$

Thus the given system of equations has only one solution
(x, y) = ((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

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