7. solve the system of equations using the elimination method.
$4x + y = 36$
$2x - y = 12$

8. solve the system of equations using the elimination method.
$4x + 2y = 6$
$-4x + 4y = 36$

9. solve the system of equations using the elimination method.
$7x + 2y = 2$
$7x - 2y = -30$

10. solve the system of equations using the elimination method.
$x + 2y = 8$
$x - 3y = 3$

11. solve the system of equations using the elimination method.
$5x + 2y = 7$
$-2x + 2y = -14$

12. solve the system of equations using the elimination method.
$-4x - 2y = -2$
$2x - 2y = -14$

Question

7. solve the system of equations using the elimination method.
$4x + y = 36$
$2x - y = 12$

8. solve the system of equations using the elimination method.
$4x + 2y = 6$
$-4x + 4y = 36$

9. solve the system of equations using the elimination method.
$7x + 2y = 2$
$7x - 2y = -30$

10. solve the system of equations using the elimination method.
$x + 2y = 8$
$x - 3y = 3$

11. solve the system of equations using the elimination method.
$5x + 2y = 7$
$-2x + 2y = -14$

12. solve the system of equations using the elimination method.
$-4x - 2y = -2$
$2x - 2y = -14$

Accepted Answer

### Problem 7:
# Explanation:
## Step1: Add the two equations to eliminate $ y $
The system is:
$$
\begin{cases}
4x + y = 36 \
2x - y = 12
\end{cases}
$$
Adding the two equations: $ (4x + y) + (2x - y) = 36 + 12 $
Simplify: $ 6x = 48 $

## Step2: Solve for $ x $
Divide both sides by 6: $ x = \frac{48}{6} = 8 $

## Step3: Substitute $ x = 8 $ into one of the original equations to find $ y $
Using $ 2x - y = 12 $: $ 2(8) - y = 12 $
Simplify: $ 16 - y = 12 $
Subtract 16 from both sides: $ -y = 12 - 16 = -4 $
Multiply both sides by -1: $ y = 4 $

# Answer:
$ x = 8 $, $ y = 4 $

### Problem 8:
# Explanation:
## Step1: Add the two equations to eliminate $ x $
The system is:
$$
\begin{cases}
4x + 2y = 6 \
-4x + 4y = 36
\end{cases}
$$
Adding the two equations: $ (4x + 2y) + (-4x + 4y) = 6 + 36 $
Simplify: $ 6y = 42 $

## Step2: Solve for $ y $
Divide both sides by 6: $ y = \frac{42}{6} = 7 $

## Step3: Substitute $ y = 7 $ into one of the original equations to find $ x $
Using $ 4x + 2y = 6 $: $ 4x + 2(7) = 6 $
Simplify: $ 4x + 14 = 6 $
Subtract 14 from both sides: $ 4x = 6 - 14 = -8 $
Divide both sides by 4: $ x = \frac{-8}{4} = -2 $

# Answer:
$ x = -2 $, $ y = 7 $

### Problem 9:
# Explanation:
## Step1: Add the two equations to eliminate $ y $
The system is:
$$
\begin{cases}
7x + 2y = 2 \
7x - 2y = -30
\end{cases}
$$
Adding the two equations: $ (7x + 2y) + (7x - 2y) = 2 + (-30) $
Simplify: $ 14x = -28 $

## Step2: Solve for $ x $
Divide both sides by 14: $ x = \frac{-28}{14} = -2 $

## Step3: Substitute $ x = -2 $ into one of the original equations to find $ y $
Using $ 7x + 2y = 2 $: $ 7(-2) + 2y = 2 $
Simplify: $ -14 + 2y = 2 $
Add 14 to both sides: $ 2y = 2 + 14 = 16 $
Divide both sides by 2: $ y = \frac{16}{2} = 8 $

# Answer:
$ x = -2 $, $ y = 8 $

### Problem 10:
# Explanation:
## Step1: Subtract the second equation from the first to eliminate $ x $
The system is:
$$
\begin{cases}
x + 2y = 8 \
x - 3y = 3
\end{cases}
$$
Subtract the second equation from the first: $ (x + 2y) - (x - 3y) = 8 - 3 $
Simplify: $ x + 2y - x + 3y = 5 $
Which becomes: $ 5y = 5 $

## Step2: Solve for $ y $
Divide both sides by 5: $ y = \frac{5}{5} = 1 $

## Step3: Substitute $ y = 1 $ into one of the original equations to find $ x $
Using $ x + 2y = 8 $: $ x + 2(1) = 8 $
Simplify: $ x + 2 = 8 $
Subtract 2 from both sides: $ x = 8 - 2 = 6 $

# Answer:
$ x = 6 $, $ y = 1 $

### Problem 11:
# Explanation:
## Step1: Subtract the second equation from the first to eliminate $ y $
The system is:
$$
\begin{cases}
5x + 2y = 7 \
-2x + 2y = -14
\end{cases}
$$
Subtract the second equation from the first: $ (5x + 2y) - (-2x + 2y) = 7 - (-14) $
Simplify: $ 5x + 2y + 2x - 2y = 7 + 14 $
Which becomes: $ 7x = 21 $

## Step2: Solve for $ x $
Divide both sides by 7: $ x = \frac{21}{7} = 3 $

## Step3: Substitute $ x = 3 $ into one of the original equations to find $ y $
Using $ 5x + 2y = 7 $: $ 5(3) + 2y = 7 $
Simplify: $ 15 + 2y = 7 $
Subtract 15 from both sides: $ 2y = 7 - 15 = -8 $
Divide both sides by 2: $ y = \frac{-8}{2} = -4 $

# Answer:
$ x = 3 $, $ y = -4 $

### Problem 12:
# Explanation:
## Step1: Add the two equations to eliminate $ y $
The system is:
$$
\begin{cases}
-4x - 2y = -2 \
2x - 2y = -14
\end{cases}
$$
Adding the two equations: $ (-4x - 2y) + (2x - 2y) = -2 + (-14) $
Simplify: $ -2x - 4y = -16 $? Wait, no, let's correct that. Wait, actually, let's add the two equations:

$ (-4x - 2y) + (2x - 2y) = -2 + (-14) $

Combine like terms: $ (-4x + 2x) + (-2y - 2y) = -16 $

Simplify: $ -2x - 4y = -16 $? No, that's not the right way. Wait, maybe I made a mistake. Wait, the coefficients of $ y $ are both -2y, so adding them will give -4y, but the coefficients of $ x $ are -4x and 2x, so -2x. But maybe a better approach: multiply the second equation by 2 to make the coefficients of $ x $ opposite? Wait, no, let's try again.

Wait, the two equations are:

1. $ -4x - 2y = -2 $
2. $ 2x - 2y = -14 $

Let's subtract the second equation from the first:

$ (-4x - 2y) - (2x - 2y) = -2 - (-14) $

Simplify: $ -4x - 2y - 2x + 2y = -2 + 14 $

Combine like terms: $ -6x = 12 $

Ah, that's better. So:

## Step1: Subtract the second equation from the first to eliminate $ y $
$ (-4x - 2y) - (2x - 2y) = -2 - (-14) $
Simplify: $ -6x = 12 $

## Step2: Solve for $ x $
Divide both sides by -6: $ x = \frac{12}{-6} = -2 $

## Step3: Substitute $ x = -2 $ into one of the original equations to find $ y $
Using $ 2x - 2y = -14 $: $ 2(-2) - 2y = -14 $
Simplify: $ -4 - 2y = -14 $
Add 4 to both sides: $ -2y = -14 + 4 = -10 $
Divide both sides by -2: $ y = \frac{-10}{-2} = 5 $

# Answer:
$ x = -2 $, $ y = 5 $

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QUESTION IMAGE

Question

Explanation:

Problem 7:

Step1: Add the two equations to eliminate \( y \)

Step2: Solve for \( x \)

Step3: Substitute \( x = 8 \) into one of the original equations to find \( y \)

Step1: Add the two equations to eliminate \( x \)

Step2: Solve for \( y \)

Step3: Substitute \( y = 7 \) into one of the original equations to find \( x \)

Step1: Add the two equations to eliminate \( y \)

Step2: Solve for \( x \)

Step3: Substitute \( x = -2 \) into one of the original equations to find \( y \)

Answer:

Problem 8: