A system of equations has infinitely many solutions. If 2y−4x=6 is one of the equations, which could be the other equation?Responsesy=4x+6y is equal to 4 x plus 6−y=−4x+6negative y is equal to negative 4 x plus 6y=2x+6y is equal to 2 x plus 6−y=−2x−3
Question
A system of equations has infinitely many solutions. If 2y−4x=6 is one of the equations, which could be the other equation?Responsesy=4x+6y is equal to 4 x plus 6−y=−4x+6negative y is equal to negative 4 x plus 6y=2x+6y is equal to 2 x plus 6−y=−2x−3
Solution
The other equation could be y=2x+3.
Here's why:
If a system of equations has infinitely many solutions, it means that the equations are dependent and represent the same line.
Given the equation 2y−4x=6, we can simplify it to y=2x+3.
So, any equation that can be simplified to the form y=2x+3 would be a valid other equation.
Looking at the options:
- y=4x+6: This equation simplifies to y=4x+6, which is not the same as y=2x+3.
- −y=−4x+6: This equation simplifies to y=4x-6, which is not the same as y=2x+3.
- y=2x+6: This equation simplifies to y=2x+6, which is not the same as y=2x+3.
- −y=−2x−3: This equation simplifies to y=2x+3, which is the same as y=2x+3.
So, the other equation could be −y=−2x−3.
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