Question

solve the following system of equations. -5x + 2y = 6 10x - 2y = -16 x = \boxed{} y = \boxed{}

Explanation:

Step1: Label the equations

Let the first equation be \( -5x + 2y = 6 \) (Equation 1) and the second be \( 10x - 2y = -16 \) (Equation 2).

Step2: Add the two equations

Adding Equation 1 and Equation 2 to eliminate \( y \):

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Step3: Solve for \( x \)

Divide both sides of \( 5x = -10 \) by 5:

$$ x = \frac{-10}{5} = -2 $$

Step4: Substitute \( x = -2 \) into Equation 1

Substitute \( x = -2 \) into \( -5x + 2y = 6 \):

$$ -5(-2) + 2y = 6\\ 10 + 2y = 6 $$

Step5: Solve for \( y \)

Subtract 10 from both sides:

$$ 2y = 6 - 10\\ 2y = -4 $$

Divide both sides by 2:

$$ y = \frac{-4}{2} = -2 $$

Answer:

\( x = -2 \), \( y = -2 \)