Hannah thinks the solution to the system below is (-4, - 6). Wirt thinks the solution is (20, 10).

2x - 3y = 10

6y = 4x - 20

A. Is Hannah correct?

B. Is Wirt correct?

Both Hannah and wirt are correct

Step-by-step explanation:

To know who is correct between them, we need to solve the given equation simultaneously

2x - 3y = 10 ... (1)

6y = 4x - 20 ... (2)

Equation 2 can be rewritten as;

4x-6y = 20 ... (3)

Solving 1 and 3 simultaneously;

2x - 3y = 10

4x - 6y = 20

It can be observed that both equations are the same, this means we only have one equation with two unknowns and when such case arises, we will have infinite number of solutions.

Given the equation

2x-3y = 10

Let k = x

Substituting k = x in the equation we will have;

2k-3y = 10

2k = 10+3y

3y = 2k-10

y = 2k-10/3

Therefore x = k, y = 2k-10/3 for any value of k.

Let's now cross check to know who is correct.

Hannah's solution was (-4,-6) that is she got x = - 4 and y = - 6.

Since k = x, then k = - 4

Substituting k = - 4 in the other equation to check if the hannah y value will correspond to calculated we have;

y = 2 (-4) - 10/3

y = - 8-10/3

y = - 6

This shows that Hannah is correct.

Similarly for wirt, her value is (20,10) i. e x = 20 y = 10

Since k = x; then k = 20

Substitituting k = 10 to confirm if the y value are the same we have

y = 2k-10/3

y = 2 (20) - 10/3

y = 40-10/3

y = 10

This shows that wirt is also correct.

Therefore both Hannah and wirt are correct.