Final answer:
The question involves solving a system of linear equations, and the correct subject is Mathematics at the High School level. The equations should be rearranged to standard linear form and solved simultaneously for x and y using appropriate algebraic methods like substitution or elimination.
Step-by-step explanation:
The correct answer is option Mathematics, specifically focusing on the topic of solving systems of linear equations. To solve the given system of equations {2x - y = 4 + 5x, x + 2y = 6 - 2y - x}, we first rearrange the equations to align with the standard form of a linear equation, y = mx + b, where 'm' represents the slope, and 'b' represents the y-intercept.
Starting with the first equation 2x - y = 4 + 5x, we can rewrite it as y = 3x + 4. For the second equation x + 2y = 6 - 2y - x, it simplifies to y = -½x + 1.5 after combining like terms and isolating y. We then solve these two new equations simultaneously to find the values of x and y that satisfy both equations.
We can use substitution or elimination methods to solve for x and y, but since both equations are already solved for y, it would be efficient to equate the two right-hand sides (3x + 4 = -½x + 1.5) and solve for x. Once we find x, we substitute it back into one of the equations to find y.
Both equations given can be rewritten in the form y = mx + b, where m is the slope and b is the y-intercept.
For the first equation, 2x - y = 4 + 5x, we can simplify it to -3x - y = 4. This equation has a slope of -3 and a y-intercept of 4.
For the second equation, x + 2y = 6 - 2y - x, we can simplify it to 2y = 6 - 2x. Dividing both sides by 2, we get y = 3 - x. This equation has a slope of -1 and a y-intercept of 3.
Therefore, both equations are linear and can be represented in the form y = mx + b.