Solve the system of equations using elimination: minus, x, plus, 3, y, equals, minus, 24−x+3y=−24 and minus, 4, x, plus, 2, y, equals, 4−4x+2y=4.

We are given the system of equations:

\[
- x + 3y = -24
\]
\[
-4x + 2y = 4
\]

### Step 1: Eliminate one of the variables
We will use the elimination method by making the coefficients of \(x\) the same in both equations. Let's eliminate \(x\).

- Multiply the first equation by 4 to match the coefficient of \(x\) in the second equation:

\[
4(- x + 3y) = 4(-24)
\]
This gives:
\[
-4x + 12y = -96
\]

Now we have the system:

\[
-4x + 12y = -96
\]
\[
-4x + 2y = 4
\]

### Step 2: Subtract the equations
Subtract the second equation from the first:

\[
(-4x + 12y) - (-4x + 2y) = -96 - 4
\]

This simplifies to:

\[
(12y - 2y) = -96 - 4
\]

\[
10y = -100
\]

### Step 3: Solve for \(y\)
Now, divide both sides by 10:

\[
y = \frac{-100}{10} = -10
\]

### Step 4: Substitute \(y = -10\) into one of the original equations
Substitute \(y = -10\) into the first equation:

\[
- x + 3(-10) = -24
\]

This simplifies to:

\[
- x - 30 = -24
\]

Add 30 to both sides:

\[
- x = 6
\]

Therefore:

\[
x = -6
\]

### Solution:
The solution to the system is:
\[
x = -6, \quad y = -10
\]

Would you like more details, or do you have any questions?

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Here are 5 related questions to consider:

1. What would happen if you tried solving the system using substitution instead of elimination?
2. How would the solution change if the first equation was altered slightly, such as by changing the constant on the right-hand side?
3. Can you graph the two equations to visually confirm the solution?
4. What if both equations had fractional coefficients? How would that affect the elimination process?
5. How would you solve the system if both equations had more variables?

**Tip:** Always double-check your solution by substituting the values back into both original equations!

Solve the system of equations using elimination: −x + 3y = −24 and −4x + 2y = 4.

Learn how to solve the system of linear equations −x + 3y = −24 and −4x + 2y = 4 using the elimination method. This problem involves key algebraic concepts, such as the elimination method and properties of linear equations. Suitable for students in Grades 8-10.

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