Question

Solve the system of equations below using elimination. You must show all work to earn full credit. −4x−6y=−24 4x+5y=24

Answer 1

To solve the system of equations using the elimination method, we start by writing down the equations clearly:

1. \(-4x - 6y = -24\) (Equation 1)
2. \(4x + 5y = 24\) (Equation 2)

### Step 1: Aligning coefficients for elimination
We want to eliminate one of the variables. A good strategy is to eliminate \(x\) by making the coefficients of \(x\) in both equations equal. Notice that the coefficient of \(x\) in Equation 1 is \(-4\) and in Equation 2 is \(4\). We can multiply Equation 2 by 1 (since it's already suitable) and Equation 1 by 1 to keep them as they are, or we can directly consider adding them since they will cancel out with the right setup.

### Step 2: Adding the equations
Let's add Equation 1 and Equation 2 directly to eliminate \(x\):

\[
(-4x - 6y) + (4x + 5y) = -24 + 24
\]

This simplifies to:

\[
(-4x + 4x) + (-6y + 5y) = 0
\]

Thus:

\[
0 - y = 0
\]

This gives us:

\[
-y = 0 \implies y = 0
\]

### Step 3: Substituting back to find \(x\)
Now that we have \(y = 0\), we can substitute this value back into one of the original equations to find \(x\). We can use Equation 2 for this:

\[
4x + 5(0) = 24
\]

This simplifies to:

\[
4x = 24
\]

Dividing both sides by 4 gives:

\[
x = 6
\]

### Step 4: Writing the solution
The solution to the system of equations is:

\[
(x, y) = (6, 0)
\]

### Conclusion
Thus, the final answer of the system of equations is \((6, 0)\).