Question

-5x+y=-33 and x+4y =-27​

Answer 1

Answer:

(5, -8)

Step-by-step explanation:

We can find the solution to the system of equations:

$\begin{cases}-5x+y\!\!\!\!&=-33\\ \ \ \ x+4y\!\!\!\!&=-27\end{cases}$

using the elimination method.

First, we can multiply both sides of the first equation by 4:

$4(-5x + y = -33)$

         ↓↓↓

$-20x + 4y = -132$

Next, we can subtract the second equation from the multiplied first equation:

$(-20x + 4y = -132)$

$\underline{-\ \ \, (x + 4y = -27)}$

$-21x + 0y = -132 - (-27)$

Using the resulting equation, we can solve for the x-coordinate of the solution:

$-21x = -132 + 27$

$-21x = -105$

     $\boxed{x = 5}$

We can now substitute this x-coordinate into one of the original equations to solve for the y-coordinate. I will use the second equation:

$x + 4y = -27$

$5 + 4y = -27$

      $4y = -32$

       $\boxed{y=-8}$

Finally, we can put these coordinates together into a solution set:

$\boxed{(5, -8)}$

Further Note

If we graph both of the equations on a Cartesian plane, the solution set is the point where the lines intersect.