Problem

Given that the system of equations $2x + y = 5$ and $3x - 2y = 7$ has a solution, find the equation of the line parallel to the line whose equation is formed by eliminating $y$ from these two equations.

Solution

Step 1 :Step 1: Eliminate $y$ from the given system of equations. Multiply the first equation by $2$ and the second equation by $1$, then subtract the second equation from the first. This gives $4x + 2y - (3x - 2y) = 10 - 7$, or $x = 3$.

Step 2 :Step 2: The equation of the line formed by eliminating $y$ is $x = 3$. This is a vertical line, so any line parallel to it will also be a vertical line and have the same form, $x = k$, where $k$ is a real number.

Step 3 :Step 3: Therefore, the equation of the line parallel to the line whose equation is formed by eliminating $y$ from the given system of equations is $x = k$, where $k$ is a real number.

From Solvely APP
Source: https://solvelyapp.com/problems/ujFRIZnGKF/

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