Question

question
solve the system of equations -2x - 7y = -14 and -x - 5y = -13 by combining the equations.
(-2x -7y = -14)
(-x -5y = -13)
-2x -7y = -14
-x -5y = -13
0 x + 0 y =
answer
attempt 1 out of 2
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Explanation:

Step1: Label the equations

Let the first equation be \( -2x - 7y = -14 \) (Equation 1) and the second equation be \( -x - 5y = -13 \) (Equation 2).

Step2: Multiply Equation 2 by 2

Multiply Equation 2 by 2 to make the coefficients of \( x \) in both equations opposite. We get \( -2x - 10y = -26 \) (Equation 3).

Step3: Subtract Equation 1 from Equation 3

Subtract Equation 1 (\( -2x - 7y = -14 \)) from Equation 3 (\( -2x - 10y = -26 \)):

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Step4: Solve for \( y \)

Divide both sides of \( -3y = -12 \) by -3:
\( y = \frac{-12}{-3} = 4 \)

Step5: Substitute \( y = 4 \) into Equation 2

Substitute \( y = 4 \) into \( -x - 5y = -13 \):
\( -x - 5(4) = -13 \)
\( -x - 20 = -13 \)

Step6: Solve for \( x \)

Add 20 to both sides: \( -x = -13 + 20 = 7 \)
Multiply both sides by -1: \( x = -7 \)

Answer:

The solution to the system is \( x = -7 \), \( y = 4 \), so the ordered pair is \( (-7, 4) \)