Question

solve each system of equations. see examples 1 and 3

1. ( x - y = 4 )

( 2x + y = 5 )

1. ( x - 2y = -2 )

( 3x + 2y = 30 )

1. ( 3x + 2y = 8 )

( x + 4y = -4 )

1. ( x - 2y = 1 )

( 2x + 3y = -12 )

1. ( 7x - 4y = -12 )

( x - 2y = 4 )

1. ( 5x + 6y = -6 )

( 7x - 3y = -54 )

1. ( 2x + 5y = -20 )

( 3x - 2y = -11 )

1. ( 4x - 3y = 17 )

( 2x - 5y = 5 )

Explanation:

Problem 15: Solve \(

$$\begin{cases} x - y = 4 \\ 2x + y = 5 \end{cases}$$

\)

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: \( y = -1 \)

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: \( y = \frac{9}{2} = 4.5 \)

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:

\( x = 3, y = -1 \)

Problem 16: Solve \(

$$\begin{cases} x - 2y = -2 \\ 3x + 2y = 30 \end{cases}$$

\)