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.

Answer

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Answer

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.

Steps

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.

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