Question

Solve the following system of equations by graphing. If this system is inconsis

identify the type of constraint.
y = 4x + 4
-12x + 3y = 3

Answer 1

Inconsistent: parallel lines.

Explanation:

Given system of equations:

`\begin{cases}y=4x+4\\-12x+3y=3\end{cases}`

Use arithmetic operations to isolate y in the second equation:

`\implies -12x+3y+12x=3+12x`

`\implies 3y=12x+3`

`\implies(3y)/(3)=(12x)/(3)+(3)/(3)`

`\implies y=4x+1`

Therefore, we can see that both equations have the same slope and so the graphs of these equations are parallel.

The solution to a system of linear equations is the point of intersection.

As parallel lines never intersect, there are no solutions to this system and the system is said to be inconsistent.