Questions: Which ordered pair is the solution to this system of equations? y=x+4 x+y=2 (-4,0) (0,2) (-1,3) (1,5)

Transcript text: Which ordered pair is the solution to this system of equations? \[ \begin{array}{l} y=x+4 \\ x+y=2 \end{array} \] $(-4,0)$ $(0,2)$ $(-1,3)$ $(1,5)$

Solution

Solution Steps

Step 1: Substitute $ y = x + 4 $ into the second equation

Substitute $ y = x + 4 $ into $ x + y = 2 $: \[ x + (x + 4) = 2 \]

Step 2: Simplify the equation

Combine like terms: \[ 2x + 4 = 2 \]

Step 3: Solve for $ x $

Subtract 4 from both sides: \[ 2x = -2 \] Divide both sides by 2: \[ x = -1 \]

Step 4: Find $ y $ using $ y = x + 4 $

Substitute $ x = -1 $ into $ y = x + 4 $: \[ y = -1 + 4 = 3 \]

Step 5: Verify the solution

The solution is $ (-1, 3) $, which matches one of the given options.

Final Answer

$\boxed{(-1, 3)}$

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