Solve the system by substitution.
minus, 4, x, minus, 4, y, equals, 24
−4x−4y=
24
3, x, plus, 10, equals, y
3x+10=
y

We are given the system of equations:

1. \( -4x - 4y = 24 \)
2. \( 3x + 10 = y \)

We can solve this system using substitution. Let's follow the steps:

### Step 1: Solve the second equation for \( y \)

From the second equation:
\[
y = 3x + 10
\]

### Step 2: Substitute \( y = 3x + 10 \) into the first equation

Now, substitute this expression for \( y \) into the first equation:

\[
-4x - 4(3x + 10) = 24
\]

### Step 3: Simplify the equation

Distribute the \( -4 \) across the terms inside the parentheses:

\[
-4x - 12x - 40 = 24
\]

Combine like terms:

\[
-16x - 40 = 24
\]

### Step 4: Solve for \( x \)

Add 40 to both sides of the equation:

\[
-16x = 64
\]

Now, divide both sides by \( -16 \):

\[
x = -4
\]

### Step 5: Substitute \( x = -4 \) into the second equation to find \( y \)

Substitute \( x = -4 \) into the second equation \( y = 3x + 10 \):

\[
y = 3(-4) + 10 = -12 + 10 = -2
\]

### Final Answer:
The solution to the system is:
\[
x = -4, \quad y = -2
\]

Would you like more details on any of the steps?

### Relative Questions:
1. How can we use substitution for systems of equations in other cases?
2. What is the advantage of solving by substitution over other methods?
3. How would the solution change if the coefficients were different?
4. Can you solve this system using the elimination method?
5. How do we interpret the solution geometrically?

### Tip:
Always double-check your solution by substituting the values of \( x \) and \( y \) back into both original equations to ensure they satisfy both.

Solve the system by substitution. −4x−4y=24 and 3x+10=y

Learn how to solve the linear system of equations -4x-4y=24 and 3x+10=y using the substitution method. This problem demonstrates key algebraic concepts such as isolating variables and solving step by step. Suitable for students in Grades 8-10.

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