Question

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?

Answer 1

2x - y = -2

x = 14 + 2y

Plug in the x equation

2(14+2y) - y = -2

Distribute

28 + 4y - y = -2

Combine variables

28 + 3y = -2

Subtract 28 on both sides

3y = -30

Divide the y

y = -10

Answer 2

X=-11

Y=8

Final: (-11,8)

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)