\( x-y=2 \) \( 0.2 x+0.4 y=1 \) The \( x \)-coordinate of the solution to the system shown is 3 6

To solve the system of equations \( x - y = 2 \) and \( 0.2x + 0.4y = 1 \), let's rewrite the first equation to express \( y \) in terms of \( x \): 1. From \( x - y = 2 \), we get \( y = x - 2 \). Substituting \( y \) in the second equation: 2. \( 0.2x + 0.4(x - 2) = 1 \). Expanding this gives: 3. \( 0.2x + 0.4x - 0.8 = 1 \). 4. Combining like terms results in \( 0.6x - 0.8 = 1 \). 5. Adding 0.8 to both sides gives \( 0.6x = 1.8 \). 6. Dividing by 0.6 gives \( x = 3 \). Thus, the \( x \)-coordinate of the solution to the system is 3. The \( y \)-coordinate can be found by substituting \( x \) back into either equation, but the focus here was on determining \( x \). So the answer is \( \mathbf{3} \) (not 6). To clarify, when solving systems like these, ensure you've rearranged correctly and pay attention to common factors that may help simplify your calculations!