Find the solution of the system of equations.

3, x, minus, 10, y, equals, minus, 46

3*x*−10*y*=

−46

8, x, plus, 10, y, equals, 24

8*x*+10*y*=

24

Let's solve the system of linear equations:

\[
\begin{aligned}
3x - 10y & = -46 \quad \text{(Equation 1)} \\
8x + 10y & = 24 \quad \text{(Equation 2)}
\end{aligned}
\]

### Step 1: Add the equations
First, add Equation 1 and Equation 2 to eliminate \( y \):

\[
(3x - 10y) + (8x + 10y) = -46 + 24
\]

Simplifying this:

\[
3x + 8x - 10y + 10y = -46 + 24
\]

\[
11x = -22
\]

### Step 2: Solve for \( x \)
Now, solve for \( x \):

\[
x = \frac{-22}{11} = -2
\]

### Step 3: Substitute \( x \) into one of the original equations
Substitute \( x = -2 \) into Equation 2:

\[
8(-2) + 10y = 24
\]

Simplify and solve for \( y \):

\[
-16 + 10y = 24
\]

\[
10y = 24 + 16 = 40
\]

\[
y = \frac{40}{10} = 4
\]

### Solution
The solution to the system of equations is:

\[
x = -2, \quad y = 4
\]

Would you like a detailed explanation of any step, or do you have any questions?

Here are 5 related questions:

1. How would you solve a system of equations using the substitution method?
2. What is the geometric interpretation of solving a system of linear equations?
3. How can you solve a system of equations using matrix methods?
4. What happens if a system of equations has no solution?
5. How can you determine if a system of equations has infinitely many solutions?

**Tip:** When solving systems of equations, always double-check your solution by substituting it back into the original equations.

Learn how to solve a system of linear equations 3x - 10y = -46 and 8x + 10y = 24 using the substitution method. Detailed step-by-step solution provided. Suitable for students in Grades 9-12.

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