Question

-3x -5y = -7-4x - 5y = 14

Answer 1

We have to solve the system of equations shown.

$\begin{gathered} -3x-5y=-7 \\ -4x-5y=14 \end{gathered}$

Let's mutliply the 2nd equation by -1,

$\begin{gathered} -1\times\lbrack-4x-5y=14\rbrack \\ 4x+5y=-14 \end{gathered}$

Now, let's add the first equation with this equation, eliminate y, and solve for x:

$\begin{gathered} -3x-5y=-7 \\ 4x+5y=-14 \\ --------- \\ 4x-3x=-14-7 \\ x=-21 \end{gathered}$

We simply plug in this value of x in the first equation and solve for y:

$\begin{gathered} -3x-5y=-7 \\ -3(-21)-5y=-7 \\ 63-5y=-7 \\ 5y=63+7 \\ 5y=70 \\ y=\frac{70}{5} \\ y=14 \end{gathered}$

Thus, the values of x and y are:

x = - 21

y = 14