How can I find 2 equations with infinitely many solutions? Thanks

The two equations would have to reduce to one same equation.

e.g.
2x + 3y = 8
4x + 6y = 16

notice the 2nd is twice the first.

Thank you

So for y= 4-2x will be 2y=8-2x?

To find two equations with infinitely many solutions, you need to create a system of equations where the two equations are dependent on each other. This means that one equation can be obtained by multiplying or adding a constant multiple of the other equation.

Let's create an example:
1) Equation 1: 2x + 3y = 6
2) Equation 2: 4x + 6y = 12

These two equations form a system. If we examine equation 2, we can see that it is obtained by multiplying equation 1 by 2:
2 * (Equation 1) leads to Equation 2.

If we solve this system of equations, we will find that the two equations are multiples of each other. This means that any solution that satisfies one equation will automatically satisfy the other equation.

To solve the system of equations:
1) Start by subtracting equation 1 from equation 2:
(4x + 6y) - (2x + 3y) = 12 - 6
Simplify and combine like terms:
2x + 3y = 6
This is the same as Equation 1.

If you notice, the second equation we obtained is identical to the first equation. This implies that any values of (x, y) that satisfy Equation 1 will automatically satisfy Equation 2, and vice versa.

Therefore, this system of equations has infinitely many solutions because the two equations are dependent on each other.