Question

Given the equation: 3x+y=4.

Write an equation of a line that would create a system of equations with the given line that has infinitely many solutions.

Answer 1

6x + 2y = 8

Explanation:

If a system of equations has an infinite number of solutions, it is called consistent dependent.

The equations of both lines will have the same slope and same y-intercept. If the two lines have the same y-intercept and the slope, they are actually in the same exact line.

Therefore, simply multiply all components of the given equation by 2 to create a second equation with the same slope and y-intercept:

6x + 2y = 8

Proof

Rearrange 6x + 2y = 8 to make y the subject:

⇒ 2y = 8 - 6x

⇒ y = 4 - 3x

And rearrange the original equation 3x + y = 4 to make y the subject:

⇒ y = 4 - 3x

So we can see that both equations rearrange to make the same equation, which means the solution to this systems of equations will give infinitely many solutions.