−8x+4y=0

Question

-x +2y = -9
solve by elimanation

Answer 1

To solve the system of equations using the elimination method, we start with the two equations:

1. $-8x+4y=0$
2. $-x+2y=-9$

Step 1: Align the equations for elimination.

We can make the second equation consistent with the first by multiplying it by 4, so that the coefficients of $y$ match.

$$4(-x+2y)=4(-9)$$

This gives us:

$$-4x+8y=-36\text{(Equation 3)}$$

Now we have:

1. $-8x+4y=0$
2. $-4x+8y=-36$

Step 2: Eliminate one variable.

We can multiply Equation 1 by 2 to line it up with Equation 3:

$$2(-8x+4y)=2(0)$$ This simplifies to:

$$-16x+8y=0\text{(Equation 4)}$$

Now we have:

4. $-16x+8y=0$
5. $-4x+8y=-36$

Step 3: Subtract Equation 3 from Equation 4.

Now we can eliminate $y$ by subtracting:

$$(-16x+8y)-(-4x+8y)=0-(-36)$$

This simplifies to:

$$-16x+4x=36$$ $$-12x=36$$

Step 4: Solve for $x$.

Divide both sides by $-12$:

$$x=\frac{36}{-12}=-3$$

Step 5: Substitute $x$ back to solve for $y$.

Now we substitute $x=-3$ back into one of the original equations. We'll use the second equation $-x+2y=-9$:

$$-(-3)+2y=-9$$ $$3+2y=-9$$ $$2y=-9-3$$ $$2y=-12$$ $$y=\frac{-12}{2}=-6$$

Solution:

The solution to the system of equations is:

$$x=-3,y=-6$$

Thus, the solution is $(x,y)=(-3,-6)$.