solve each system of equations. see examples 1 and 3
15. ( x - y = 4 )
( 2x + y = 5 )
16. ( x - 2y = -2 )
( 3x + 2y = 30 )
17. ( 3x + 2y = 8 )
( x + 4y = -4 )
18. ( x - 2y = 1 )
( 2x + 3y = -12 )
19. ( 7x - 4y = -12 )
( x - 2y = 4 )
20. ( 5x + 6y = -6 )
( 7x - 3y = -54 )
21. ( 2x + 5y = -20 )
( 3x - 2y = -11 )
22. ( 4x - 3y = 17 )
( 2x - 5y = 5 )

Question

solve each system of equations. see examples 1 and 3
15. ( x - y = 4 )
    ( 2x + y = 5 )
16. ( x - 2y = -2 )
    ( 3x + 2y = 30 )
17. ( 3x + 2y = 8 )
    ( x + 4y = -4 )
18. ( x - 2y = 1 )
    ( 2x + 3y = -12 )
19. ( 7x - 4y = -12 )
    ( x - 2y = 4 )
20. ( 5x + 6y = -6 )
    ( 7x - 3y = -54 )
21. ( 2x + 5y = -20 )
    ( 3x - 2y = -11 )
22. ( 4x - 3y = 17 )
    ( 2x - 5y = 5 )

Accepted Answer

### Problem 15: Solve $ \begin{cases} x - y = 4 \ 2x + y = 5 \end{cases} $
# Explanation:
## Step 1: Eliminate $ y $ by adding the two equations.
Add the equations $ x - y = 4 $ and $ 2x + y = 5 $:
$ (x - y) + (2x + y) = 4 + 5 $
Simplify: $ 3x = 9 $

## Step 2: Solve for $ x $.
Divide both sides by 3: $ x = \frac{9}{3} = 3 $

## Step 3: Substitute $ x = 3 $ into $ x - y = 4 $ to find $ y $.
$ 3 - y = 4 $
Subtract 3 from both sides: $ -y = 1 $
Multiply by -1: $ y = -1 $
# Answer: $ x = 3, y = -1 $

### Problem 16: Solve $ \begin{cases} x - 2y = -2 \ 3x + 2y = 30 \end{cases} $
# Explanation:
## Step 1: Eliminate $ y $ by adding the two equations.
Add $ x - 2y = -2 $ and $ 3x + 2y = 30 $:
$ (x - 2y) + (3x + 2y) = -2 + 30 $
Simplify: $ 4x = 28 $

## Step 2: Solve for $ x $.
Divide by 4: $ x = \frac{28}{4} = 7 $

## Step 3: Substitute $ x = 7 $ into $ x - 2y = -2 $ to find $ y $.
$ 7 - 2y = -2 $
Subtract 7: $ -2y = -9 $
Divide by -2: $ y = \frac{9}{2} = 4.5 $
# Answer: $ x = 7, y = 4.5 $

### Problem 17: Solve $ \begin{cases} 3x + 2y = 8 \ x + 4y = -4 \end{cases} $
# Explanation:
## Step 1: Eliminate $ y $ by multiplying the first equation by 2.
Multiply $ 3x + 2y = 8 $ by 2: $ 6x + 4y = 16 $

## Step 2: Subtract the second equation from the new equation.
Subtract $ x + 4y = -4 $ from $ 6x + 4y = 16 $:
$ (6x + 4y) - (x + 4y) = 16 - (-4) $
Simplify: $ 5x = 20 $

## Step 3: Solve for $ x $.
Divide by 5: $ x = \frac{20}{5} = 4 $

## Step 4: Substitute $ x = 4 $ into $ x + 4y = -4 $ to find $ y $.
$ 4 + 4y = -4 $
Subtract 4: $ 4y = -8 $
Divide by 4: $ y = -2 $
# Answer: $ x = 4, y = -2 $

### Problem 18: Solve $ \begin{cases} x - 2y = 1 \ 2x + 3y = -12 \end{cases} $
# Explanation:
## Step 1: Solve $ x - 2y = 1 $ for $ x $.
$ x = 2y + 1 $

## Step 2: Substitute $ x = 2y + 1 $ into $ 2x + 3y = -12 $.
$ 2(2y + 1) + 3y = -12 $
Expand: $ 4y + 2 + 3y = -12 $
Simplify: $ 7y + 2 = -12 $

## Step 3: Solve for $ y $.
Subtract 2: $ 7y = -14 $
Divide by 7: $ y = -2 $

## Step 4: Substitute $ y = -2 $ into $ x = 2y + 1 $ to find $ x $.
$ x = 2(-2) + 1 = -4 + 1 = -3 $
# Answer: $ x = -3, y = -2 $

### Problem 19: Solve $ \begin{cases} 7x - 4y = -12 \ x - 2y = 4 \end{cases} $
# Explanation:
## Step 1: Solve $ x - 2y = 4 $ for $ x $.
$ x = 2y + 4 $

## Step 2: Substitute $ x = 2y + 4 $ into $ 7x - 4y = -12 $.
$ 7(2y + 4) - 4y = -12 $
Expand: $ 14y + 28 - 4y = -12 $
Simplify: $ 10y + 28 = -12 $

## Step 3: Solve for $ y $.
Subtract 28: $ 10y = -40 $
Divide by 10: $ y = -4 $

## Step 4: Substitute $ y = -4 $ into $ x = 2y + 4 $ to find $ x $.
$ x = 2(-4) + 4 = -8 + 4 = -4 $
# Answer: $ x = -4, y = -4 $

### Problem 20: Solve $ \begin{cases} 5x + 6y = -6 \ 7x - 3y = -54 \end{cases} $
# Explanation:
## Step 1: Eliminate $ y $ by multiplying the second equation by 2.
Multiply $ 7x - 3y = -54 $ by 2: $ 14x - 6y = -108 $

## Step 2: Add to the first equation.
Add $ 5x + 6y = -6 $ and $ 14x - 6y = -108 $:
$ (5x + 6y) + (14x - 6y) = -6 + (-108) $
Simplify: $ 19x = -114 $

## Step 3: Solve for $ x $.
Divide by 19: $ x = \frac{-114}{19} = -6 $

## Step 4: Substitute $ x = -6 $ into $ 5x + 6y = -6 $ to find $ y $.
$ 5(-6) + 6y = -6 $
Simplify: $ -30 + 6y = -6 $
Add 30: $ 6y = 24 $
Divide by 6: $ y = 4 $
# Answer: $ x = -6, y = 4 $

### Problem 21: Solve $ \begin{cases} 2x + 5y = -20 \ 3x - 2y = -11 \end{cases} $
# Explanation:
## Step 1: Eliminate $ y $ by multiplying the first equation by 2 and the second by 5.
First equation ×2: $ 4x + 10y = -40 $
Second equation ×5: $ 15x - 10y = -55 $

## Step 2: Add the two new equations.
$ (4x + 10y) + (15x - 10y) = -40 + (-55) $
Simplify: $ 19x = -95 $

## Step 3: Solve for $ x $.
Divide by 19: $ x = \frac{-95}{19} = -5 $

## Step 4: Substitute $ x = -5 $ into $ 2x + 5y = -20 $ to find $ y $.
$ 2(-5) + 5y = -20 $
Simplify: $ -10 + 5y = -20 $
Add 10: $ 5y = -10 $
Divide by 5: $ y = -2 $
# Answer: $ x = -5, y = -2 $

### Problem 22: Solve $ \begin{cases} 4x - 3y = 17 \ 2x - 5y = 5 \end{cases} $
# Explanation:
## Step 1: Eliminate $ x $ by multiplying the second equation by 2.
Multiply $ 2x - 5y = 5 $ by 2: $ 4x - 10y = 10 $

## Step 2: Subtract from the first equation.
Subtract $ 4x - 10y = 10 $ from $ 4x - 3y = 17 $:
$ (4x - 3y) - (4x - 10y) = 17 - 10 $
Simplify: $ 7y = 7 $

## Step 3: Solve for $ y $.
Divide by 7: $ y = 1 $

## Step 4: Substitute $ y = 1 $ into $ 2x - 5y = 5 $ to find $ x $.
$ 2x - 5(1) = 5 $
Simplify: $ 2x - 5 = 5 $
Add 5: $ 2x = 10 $
Divide by 2: $ x = 5 $
# Answer: $ x = 5, y = 1 $

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QUESTION IMAGE

Question

Explanation:

Problem 15: Solve \(

Step 1: Eliminate \( y \) by adding the two equations.

Step 2: Solve for \( x \).

Step 3: Substitute \( x = 3 \) into \( x - y = 4 \) to find \( y \).

Step 1: Eliminate \( y \) by adding the two equations.

Step 2: Solve for \( x \).

Step 3: Substitute \( x = 7 \) into \( x - 2y = -2 \) to find \( y \).

Step 1: Eliminate \( y \) by multiplying the first equation by 2.

Step 2: Subtract the second equation from the new equation.

Step 3: Solve for \( x \).

Step 4: Substitute \( x = 4 \) into \( x + 4y = -4 \) to find \( y \).

Answer:

Problem 16: Solve \(