Solve the system of equations.

Question

4x−8y=−36
−6x+y=32 (1 point)
(, )

Answer 1

To solve the system of equations given by:

1. $4x-8y=-36$ (Equation 1)
2. $-6x+y=32$ (Equation 2)

Let's start by rewriting both equations.

Step 1: Isolate $y$ in Equation 2.

From Equation 2: $$y=6x+32$$

Step 2: Substitute $y$ in Equation 1.

Now, substitute $y$ from Equation 2 into Equation 1: $$4x-8(6x+32)=-36$$

Step 3: Simplify the equation. $$4x-48x-256=-36$$ $$-44x-256=-36$$

Step 4: Solve for $x$. Add 256 to both sides: $$-44x=220$$

Now divide by -44: $$x=-\frac{220}{44}=-5$$

Step 5: Substitute $x$ back to find $y$.

Using Equation 2: $$y=6(-5)+32$$ $$y=-30+32=2$$

Final Solution:

The solution to the system of equations is: $$(x,y)=(-5,2)$$

Thus, the final answer is: $$\boxed{{\displaystyle (-5,2)}}$$