Question

solve the system of equations -3x - 2y = -14 and -x - 7y = -11 by combining the equations. \\(-3x - 2y = -14\\) \\((-x - 7y = -11)\\) \\(-3x - 2y = -14\\) \\(-x - 7y = -11\\) \\(x + \square y = \square\\)

Explanation:

Step1: Label the equations

Let the first equation be \( -3x - 2y = -14 \) (Equation 1) and the second equation be \( -x - 7y = -11 \) (Equation 2).

Step2: Eliminate x

Multiply Equation 2 by 3: \( 3(-x - 7y)=3(-11) \), which simplifies to \( -3x - 21y = -33 \) (Equation 3).

Step3: Subtract Equation 1 from Equation 3

\( (-3x - 21y)-(-3x - 2y)= -33 - (-14) \)
Simplify left side: \( -3x - 21y + 3x + 2y = -19y \)
Simplify right side: \( -33 + 14 = -19 \)
So, \( -19y = -19 \)

Step4: Solve for y

Divide both sides by -19: \( y = \frac{-19}{-19}=1 \)

Step5: Substitute y into Equation 2

\( -x - 7(1)= -11 \)
Simplify: \( -x - 7 = -11 \)
Add 7 to both sides: \( -x = -11 + 7 = -4 \)
Multiply both sides by -1: \( x = 4 \)

Answer:

The solution to the system is \( x = 4 \) and \( y = 1 \), so the ordered pair is \( (4, 1) \)