Question

solve the system of equations by the addition method.
\

$$\begin{cases} x + y = 7 \\\\ x - y = -9 \\end{cases}$$

Explanation:

Step1: Add the two equations

Add the equations \( x + y = 7 \) and \( x - y = -9 \) together.

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Step2: Solve for x

Divide both sides of \( 2x = -2 \) by 2.

$$ x = \frac{-2}{2} = -1 $$

Step3: Substitute x into one equation

Substitute \( x = -1 \) into the first equation \( x + y = 7 \).

$$ -1 + y = 7 $$

Step4: Solve for y

Add 1 to both sides of the equation \( -1 + y = 7 \).

$$ y = 7 + 1 = 8 $$

Answer:

The solution to the system is \( x = -1 \), \( y = 8 \) (or as an ordered pair \((-1, 8)\)).