Determine which equations below when combined with the equation 3x - 4y equals two or form a system with no solutions. choose all that apply.1. 2y=1.5x-22. 2y=1.5-13. 3x+4y=24. -4y+3x=-2

The correct answers are:

1. 2y=1.5x-2 ; and 4. -4y+3x=-2.

Explanation:

Using the first equation, we have the system

The second equation can be written in standard form just as the first one.  To do this, we will subtract 1.5x from each side:

2y = 1.5x-2

2y-1.5x = 1.5x-2-1.5x

-1.5x+2y = -2

This makes our system

To solve this, we will make the coefficients of x the same; we do this by multiplying the bottom equation by 2:

2(-1.5x+2y=-2)

-3x+4y=-4

This gives us the system

We solve this by adding the two equations:

There is no solution to this.

For the second system, we will follow the same process, subtract 1.5x from each side of the second equation:

2y=1.5x-1

2y-1.5x = 1.5x-1-1.5x

-1.5x+2y = -1

To make the coefficients of x the same, multiply the second equation by 2:

2(-1.5x+2y=-1)

-3x+4y=-2

We will add the two equations to solve:

This means that the equations are of the same line and there are infinite solutions.

For the third system, the coefficients are already the same.  We will cancel by subtracting the bottom equation from the top:

Since we have a value for y, this has a solution.

For the last system, we will rearrange the second equation with the x term in front:

3x-4y=-2

Now we will subtract this from the first equation:

This has no solution.

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step-by-step explanation: then we will answer