Question

Is the system of equations consistent and independent, consistent and dependent, or inconsistent?

Answer 1

Since the given system has exactly one solution i,e (-10,22) so, the system is consistent and independent.

Step-by-step explanation:

We need to solve the system of equations and identify if the system of equations are consistent and independent, consistent and dependent, or inconsistent.

The system of equations given are:

$y=-x+12\\y=-2x+2$

We can solve using substitution method.

Let $y=-x+12\,\,eq(1)\\y=-2x+2\,\,eq(2)$

Putting value of y fom eq(2) into eq(1)

$-2x+2=-x+12$

Finding value of x:

$-2x+2=-x+12\\-2x+x=12-2\\-x=10\\x=-10$

So, value of x = -10.

Putting value of x in eq(1) to find value of y

$y=-x+12$

$y=-(-10)+12$

$y=10+12$

$y=22$

So, value of y= 22

If a system has exactly one solution then the system is consistent and independent.

Since the given system has exactly one solution i,e (-10,22) so, the system is consistent and independent.

Keywords: System of equations

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