Question

2x - y = 5 x + 3y = 7 What is the value of the system determinant?

Answer 1

7

Step-by-step explanation:

When finding the system determinant you take both of the x-coefficients and put them in the 1st column and then the y-coefficients in the 2nd column.

Always start with the first equation when ordering this

2x - y = 5

x + 3y = 7

2x and 1x are your x-coefficients

-1y and 3y are your y-coefficients

Column 1 is both of the x-coefficients and the number at the top of the column will always be from the first equation.

Column 2 is both of the y-coefficients and the number at the top of the column will always be from the first equation.

C1 = Column 1

C2 = Column 2

C1 C2

Row 1 [2 -1]

Row 2 [1 3]

First multiply Column 1 ,Row 1 by Column 2 ,Row 2

2 × 3 = 6

And then cross multiply again with the two remainding numbers 1 and 1

-1 × 1 = -1

After cross multiplying the columns you take the number that you got by multiplying Column 1, Row 1 and Column 2, Row 2 (6) and you will subtract it by the answer you got from multiplying Column 1, Row 2 and Column 2, Row 1 (-1).

Then you will take your number from the first equation and subract it by the number you got in the second equation

6 - (-1) = 7

Remember that when subtracting the order matters and if you do not subtract in this order you will get a different answer.

Answer 2

2x - y = 5
x + 3y = 7

I'm assuming you mean the coefficient matrix.

`\left[\begin{array}{ccc}2&-1\\1&3\end{array}\right] =(2)(3)-(-1)(1)=6+1=7`