Given the system of equations:

3x = - 1 - 4y

2x + 3y = 14

What is the value of the system determinant?

What is the value of the x-determinant?

What is the value of the y-determinant?

What is the solution to the system of equations?

X=-11

Y=8

Final: (-11,8)

Step-by-step explanation:

Isolate the Y variable

3x = - 1 - 4y

3x - 1 = - 4y

divide by - 4

y = - 3/4x - 1/4

Next equation, do the same thing

2x + 3y = 14

3y = 14 - 2x

divide by 3

y = 4 2/3 - 2/3x

Set the two equations (that are set equal to Y) equal to each other

-3/4x - 1/4 = 4 2/3 - 2/3x

+ 1/4 + 1/4

-3/4x = 11/12 - 2/3x

+2/3x + 2/3x

-1/12x = 11/12

Now divide both sides by - 1/12

x = - 11

(11/12 was found by finding the LCM (Least Common Multiple) of 3 and 4, which is 12 and getting the equivalent factor for the denominator of 12. Same went for the - 1/12)

Plug - 11 in for x for one of the previous equations

3 (-11) = - 1 - 4y

-33 = - 1 - 4y

+1 + 1

-32 = - 4y

Divide both sides by - 4

y = 8

(-11,8)