Questions: Which ordered pair is the solution to this system of equations? 2x - y = 10 x + y = 2 (4,2) (4,-2) (2,-4) (-4,2)

Transcript text: 8 Multile Choice 2 points Which ordered pair is the solution to this system of equations? \[ \begin{aligned} 2 x-y & =10 \\ x+y & =2 \end{aligned} \] $(4,2)$ $(4,-2)$ $(2,-4)$ $(-4,2)$

Solution

Solution Steps

Step 1: Solve one of the equations for one variable

We will solve the second equation $ x + y = 2 $ for $ x $: \[ x = 2 - y \]

Step 2: Substitute the expression into the other equation

Substitute $ x = 2 - y $ into the first equation $ 2x - y = 10 $: \[ 2(2 - y) - y = 10 \]

Step 3: Simplify and solve for $ y $

Expand and simplify the equation: \[ 4 - 2y - y = 10 \] \[ 4 - 3y = 10 \] \[ -3y = 6 \] \[ y = -2 \]

Step 4: Substitute $ y $ back to find $ x $

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

Step 5: Verify the solution

The solution is $ (4, -2) $, which matches one of the given options.

Final Answer

$\boxed{(4, -2)}$

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