Question

Solve the following system of equations by graphing. Then determine whether the system is consistent or inconsistent and whether theequations are dependent or independent. If the system is consistent, give the solution.- 6x + 6y = -24- 4x + 4y = -12

Answer 1

Given:

- 6x + 6y = -24

- 4x + 4y = -12

Simplest form of the above equation is,

- x +y = -4

y=x-4 .................. (1)

- x + y = -3

y=x-3 .................. (2)

Let us find some points for the (1) equation.y=x-4

When x=1, we get, y=-3

When x=2, we get, y=-2

When x=3, we get, y=-1

(1, -3), (2, -2), and (3, -1).

Let us find some points for the (2) equation.

When x=1, we get y=-2

When x=2, we get y=-1

When x=3, we get y=0

(1, -2), (2, -1), and (3, 0).

Hence, the graph is,

Sicne, line are parallel.

Hence, the system is inconsistent.

That is, the system has no solution.

The linear equations in the slope intercept form is,

y= x+ (-4)

y= x+ (-3)