Question

1 ( 3x + 2y = 11 )
( 7x - y = 3 )
2 ( 3x - 4y = 18 )
( x + 3y = -7 )
3 ( 5x + 2y = -8 )
( 9x - 4y = -22 )
4 ( x - 5y = 15 )
( 4x - 3y = 26 )
5 ( 2x + 5y = 11 )
( -3x + 8y = -1 )
6 ( 7x - 3y = 2 )
( 5x + 4y = -17 )
7 ( 4x - 5y = -28 )
( -9x - 2y = 10 )
8 ( 2x + 3y = 10 )
( 3x - 10y = 15 )
9 ( -7x + 4y = -6 )
( 2x - 5y = 21 )
10 ( 8x + 3y = -12 )
( 6x + 5y = -20 )
11 ( -4x - 9y = 1 )
( -x + 2y = -4 )
12 ( 5x - 12y = -16 )
( -3x + 4y = 0 )

Explanation:

Let's solve problem 1: \(

$$\begin{cases} 3x + 2y = 11 \\ 7x - y = 3 \end{cases}$$

\)

Step1: Solve the second equation for \( y \)

From \( 7x - y = 3 \), we get \( y = 7x - 3 \).

Step2: Substitute \( y = 7x - 3 \) into the first equation

Substitute into \( 3x + 2y = 11 \):
\( 3x + 2(7x - 3) = 11 \)
Expand: \( 3x + 14x - 6 = 11 \)
Combine like terms: \( 17x - 6 = 11 \)
Add 6 to both sides: \( 17x = 17 \)
Divide by 17: \( x = 1 \).

Step3: Substitute \( x = 1 \) back into \( y = 7x - 3 \)

\( y = 7(1) - 3 = 4 \).

Answer:

The solution is \( (1, 4) \)