10*x*−2*y*=

44

minus, 2, x, minus, 9, y, equals, 10

−2*x*−9*y*=

10

It appears you're working with a system of two equations involving variables \( x \) and \( y \):

1. \( 10x - 2y = 44 \)
2. \( -2x - 9y = 10 \)

Let's solve this system step by step.

### Step 1: Solve the first equation for \( x \)

From the first equation:
\[
10x - 2y = 44
\]
Solve for \( x \):
\[
10x = 44 + 2y
\]
\[
x = \frac{44 + 2y}{10}
\]
\[
x = 4.4 + 0.2y
\]

### Step 2: Substitute \( x \) into the second equation

Now substitute \( x = 4.4 + 0.2y \) into the second equation \( -2x - 9y = 10 \):
\[
-2(4.4 + 0.2y) - 9y = 10
\]
Distribute the \( -2 \):
\[
-8.8 - 0.4y - 9y = 10
\]
Combine the terms with \( y \):
\[
-8.8 - 9.4y = 10
\]
Now, solve for \( y \):
\[
-9.4y = 10 + 8.8
\]
\[
-9.4y = 18.8
\]
\[
y = \frac{18.8}{-9.4} = -2
\]

### Step 3: Solve for \( x \)

Now that we know \( y = -2 \), substitute this value back into the equation for \( x \):
\[
x = 4.4 + 0.2(-2)
\]
\[
x = 4.4 - 0.4 = 4
\]

### Solution:

The solution to the system of equations is:
\[
x = 4, \quad y = -2
\]

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

### Related Questions:
1. How can I solve a system of equations using substitution?
2. What happens if the coefficients of \( x \) and \( y \) are the same in both equations?
3. How can I solve a system of equations using elimination?
4. What is the graphical method of solving a system of linear equations?
5. What happens if the system of equations has no solution or infinitely many solutions?

### Tip:
When solving systems of equations, always check your solution by substituting the values of \( x \) and \( y \) back into both original equations to verify correctness.

Explore how to solve a system of linear equations with two variables, x and y, using substitution. This problem involves equations 10x - 2y = 44 and -2x - 9y = 10, breaking down the solution step by step. Suitable for students in Grades 8-10.

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