Question

Are the equations 2x - y = - 4 and 3x + y = -1 dependent, independent or neither

Answer 1

Answer:

From the above calculations, it is clear that the consistent system has exactly one solution i.e. x = -1, y =2, therefore, it is independent.

Step-by-step explanation:

Given the system of equations

$\begin{bmatrix}2x-y=-4\\ 3x+y=-1\end{bmatrix}$

$\mathrm{Multiply\:}2x-y=-4\mathrm{\:by\:}3\:\mathrm{:}\:\quad \:6x-3y=-12$

$\mathrm{Multiply\:}3x+y=-1\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:6x+2y=-2$

$\begin{bmatrix}6x-3y=-12\\ 6x+2y=-2\end{bmatrix}$

$6x+2y=-2$

$-$

$\underline{6x-3y=-12}$

$5y=10$

so the system of equations becomes

$\begin{bmatrix}6x-3y=-12\\ 5y=10\end{bmatrix}$

solving 5y = 10 for y

$5y=10$

Divide both sides by 5

$\frac{5y}{5}=\frac{10}{5}$

simplify

$y=2$

$\mathrm{For\:}6x-3y=-12\mathrm{\:plug\:in\:}y=2$

$6x-3\cdot \:2=-12$

$6x-6=-12$

Adding 6 to both sides

$6x-6+6=-12+6$

$6x=-6$

Divide both sides by 6

$\frac{6x}{6}=\frac{-6}{6}$

$x=-1$

Therefore, the solution to the system of equations be:

$x=-1,\:y=2$

From the above calculations, it is clear that the consistent system has exactly one solution i.e. x = -1, y =2, therefore, it is independent.