Question

For the system shown, what is the value of y-x ?

x+\frac{3}{4}y=-14

-4x+3y=-16

Answer 1

There is no solution for the given system of equations, making it impossible to determine the value of y-x.

Step-by-step explanation:

To find the value of y-x for the given system of equations:

First, solve the system of equations by either substitution or elimination.

Let's use elimination. Multiply the first equation by 4 and the second equation by 3 to eliminate the coefficients of x. The resulting equations are:

4x + 3y = -56

-12x + 9y = -48

Add the two equations together to eliminate x:

4x - 12x + 3y + 9y = -56 - 48

-8x + 12y = -104

Now, divide the equation by 4 to simplify it further:

-2x + 3y/4 = -26

From the first equation, we can express x in terms of y:

x = (3y/4) + 14

Substitute this value of x into the second equation:

-4((3y/4) + 14) + 3y = -16

-3y - 56 + 3y = -16

-56 = -16

As you can see, the two equations are inconsistent, and there is no solution.

Therefore, we cannot determine the value of y-x for this system of equations.

Answer 2

The value of y-x is -7

Step-by-step explanation:

To find the value of y-x for the given system of equations:

x + {3}/{4}y = -14

-4x + 3y = -16

We can solve this system of equations by substitution or elimination.

Let's use the elimination method.

Multiply the first equation by 4 to eliminate the fraction:

4x + 3y = -56

-4x + 3y = -16

Add the two equations to eliminate x:

6y = -72

Divide both sides by 6:

y = -12

Now substitute the value of y into the first equation:

x + {3}/{4}(-12) = -14

x - 9 = -14

Add 9 to both sides:

x = -5

So, the value of y - x is:

-12 - (-5)

= -12 + 5

= -7